Updated on 2024/04/20

写真a

 
HOSHI Akinari
 
Organization
Academic Assembly Institute of Science and Technology Fundamental Sciences Professor
Graduate School of Science and Technology Fundamental Sciences Professor
Faculty of Science Department of Science Professor
Title
Professor
Homepage
http://mathweb.sc.niigata-u.ac.jp/~hoshi/
External link

Degree

  • Ph.D. ( 2005.3   Waseda University )

Research Interests

  • Number Theory

  • Algebra

  • 代数幾何

  • 整数論

  • Arithmetic Geometry

  • Algebraic Geometry

  • 数論幾何

Research Areas

  • Natural Science / Algebra

Research History (researchmap)

  • Niigata University   Mathematical Science, Fundamental Sciences, Graduate School of Science and Technology   Chair

    2023.4

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  • Niigata University   Department of Mathematics   Vice Chair

    2023.4 - 2024.3

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  • Niigata University   Faculty of Science Department of Science   Chair

    2022.4 - 2023.3

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  • Niigata University   Department of Mathematics   Professor

    2021.8

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    Country：Japan

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  • Niigata University   Department of Mathematics   Associate Professor

    2017.4 - 2021.8

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    Country：Japan

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  • Niigata University   Department of Mathematics   Associate Professor

    2013.4 - 2017.3

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    Country：Japan

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  • Rikkyo University   Department of Mathematics   Assistant Professor

    2008.4 - 2013.3

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  • Waseda University   Department of Mathematics   Research Associate

    2006.4 - 2008.3

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  • Japan Society for the Promotion of Science   Research Fellow (PD)

    2005.4 - 2006.3

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  • University of Regensburg   Guest Researcher

    2004.9 - 2005.8

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  • Japan Society for the Promotion of Science   Reseach Fellow (DC2)

    2004.4 - 2005.3

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Research History

  • Niigata University   Fundamental Sciences, Institute of Science and Technology, Academic Assembly   Professor

    2021.8

  • Niigata University   Graduate School of Science and Technology Fundamental Sciences   Professor

    2021.8

  • Niigata University   Faculty of Science Department of Science   Professor

    2021.8

  • Niigata University   Faculty of Science Department of Science   Associate Professor

    2017.4 - 2021.8

  • Niigata University   Graduate School of Science and Technology Fundamental Sciences   Associate Professor

    2013.4 - 2021.8

  • Niigata University   Faculty of Science Department of Mathematics   Associate Professor

    2013.4 - 2017.3

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Education

  • Waseda University   Department of Mathematical Sciences   Ph.D. (Doctor of Science)

    2003.4 - 2005.3

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    Country： Japan

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  • Waseda University   Department of Mathematical Sciences   Master of Science

    2001.4 - 2003.3

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  • Waseda University   Department of Mathematics   Bachelor of Science

    1997.4 - 2001.3

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    Country： Japan

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Professional Memberships

Committee Memberships

  • Mathematical Society of Japan   Local Delegate  

    2023.3 - 2024.2   

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Papers

  • Rationality problem for norm one tori for dihedral extensions Reviewed

    Akinari Hoshi, Aiichi Yamasaki

    Journal of Algebra   640   368 - 384   2024.2

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    Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jalgebra.2023.10.034

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  • Rationality problem of two-dimensional quasi-monomial group actions Reviewed

    Akinari Hoshi, Hidetaka Kitayama

    To appear in Transformation Groups   2024

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  • Multiplicative Invariant Fields of Dimension ≤ 6 Reviewed International coauthorship

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    Memoirs of the American Mathematical Society   283 ( 1403 )   1 - 137   2023.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Mathematical Society (AMS)  

    <p>The finite subgroups of are classified up to conjugation in Brown, Büllow, Neubüser, Wondratscheck, and Zassenhaus (1978); in particular, there exist non-conjugate finite groups in . Each finite group of acts naturally on ; thus we get a faithful -lattice with . In this way, there are exactly such lattices. Given a -lattice with , the group acts on the rational function field by multiplicative actions, i.e. purely monomial automorphisms over . We are concerned with the rationality problem of the fixed field . A tool of our investigation is the unramified Brauer group of the field over . It is known that, if the unramified Brauer group, denoted by , is non-trivial, then the fixed field is not rational (= purely transcendental) over . A formula of the unramified Brauer group for the multiplicative invariant field was found by Saltman in 1990. However, to calculate for a specific multiplicatively invariant field requires additional efforts, even when the lattice is of rank equal to . There is a direct decomposition where is some subgroup of . The first summand , which is related to the faithful linear representations of , has been investigated by many authors. But the second summand doesn’t receive much attention except when the rank is . Theorem 1. Among the finite groups , let be the associated faithful -lattice with , there exist precisely lattices with . In these situations, and thus . The groups are isomorphic to , , , , whose GAP IDs are (4,12,4,12), (4,32,1,2), (4,32,3,2), (4,33,3,1), (4,33,6,1) respectively in Brown, Büllow, Neubüser, Wondratscheck, and Zassenhaus (1978) and in The GAP Group (2008). Theorem 2. There exist (resp. ) finite subgroups in (resp. ). Let be the lattice with rank (resp. ) associated to each group . Among these lattices precisely (resp. ) of them satisfy the condition . The GAP IDs (actually the CARAT IDs) of the corresponding groups may be determined explicitly. Motivated by these results, we construct -lattices of rank , , ( is any positive integer and is any odd prime number) satisfying that and ; and therefore are not rational over . For these -lattices , we prove that the flabby class of is not invertible. We also construct an example of -lattice (resp. -lattice) of rank (resp. ) with . As a consequence, we give a counter-example to Noether’s problem for over where is some abelian group.</p>

    DOI： 10.1090/memo/1403

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  • Norm one tori and Hasse norm principle, II: Degree 12 case Reviewed

    Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

    Journal of Number Theory   244   84 - 110   2023.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jnt.2022.09.006

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  • Davenport and Hasse's theorems and lifts of multiplication matrices of Gaussian periods Reviewed

    Akinari Hoshi, Kazuki Kanai

    Finite Fields and Their Applications   84 ( 102101 )   1 - 26   2022.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.ffa.2022.102101

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  • Norm one Tori and Hasse norm principle Reviewed

    Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

    Mathematics of Computation   91 ( 337 )   2431 - 2458   2022.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Mathematical Society (AMS)  

    <p>Let be a field and be an algebraic -torus. In 1969, over a global field , Voskresenskiǐ proved that there exists an exact sequence where is the kernel of the weak approximation of , is the Shafarevich-Tate group of , is a smooth -compactification of , , is the Picard group of and stands for the Pontryagin dual. On the other hand, in 1963, Ono proved that for the norm one torus of , if and only if the Hasse norm principle holds for . First, we determine for algebraic -tori up to dimension . Second, we determine for norm one tori with and . We also show that for when the Galois group of the Galois closure of is the Mathieu group with . Third, we give a necessary and sufficient condition for the Hasse norm principle for with and . As applications of the results, we get the group of -equivalence classes over a local field via Colliot-Thélène and Sansuc’s formula and the Tamagawa number over a number field via Ono’s formula .</p>

    DOI： 10.1090/mcom/3735

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    Other Link： https://www.ams.org/mcom/2022-91-337/S0025-5718-2022-03735-2/S0025-5718-2022-03735-2.pdf

  • A two-dimensional rationality problem and intersections of two quadrics Reviewed International coauthorship

    Akinari Hoshi, Ming-Chang Kang, Hidetaka Kitayama, Aiichi Yamasaki

    manuscripta mathematica   168 ( 3-4 )   423 - 437   2022.7

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    Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s00229-021-01313-7

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    Other Link： https://link.springer.com/article/10.1007/s00229-021-01313-7/fulltext.html

  • Rationality problem for norm one tori Reviewed

    Akinari Hoshi, Aiichi Yamasaki

    Israel Journal of Mathematics   241 ( 2 )   849 - 867   2021.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s11856-021-2117-1

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    Other Link： https://link.springer.com/article/10.1007/s11856-021-2117-1/fulltext.html

  • On Lecacheux’s family of quintic polynomials Reviewed

    Akinari Hoshi, Masakazu Koshiba

    Proceedings of the Japan Academy, Series A, Mathematical Sciences   97 ( 1 )   1 - 6   2021.1

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Project Euclid  

    DOI： 10.3792/pjaa.97.001

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  • Noether’s problem and rationality problem for multiplicative invariant fields: a survey Reviewed

    Akinari Hoshi

    RIMS Kôkyûroku Bessatsu   B77   29 - 53   2020.4

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  • Three-dimensional purely quasimonomial actions Reviewed

    Akinari Hoshi, Hidetaka Kitayama

    Kyoto J. Math.   60 ( 1 )   335 - 377   2020.4

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1215/21562261-2019-0008

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  • Rationality problem for norm one tori in small dimensions Reviewed

    Sumito Hasegawa, Akinari Hoshi, Aiichi Yamasaki

    Math. Comp.   89   923 - 940   2020.3

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1090/mcom/3469

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  • Degree three unramified cohomology groups and Noether's problem for groups of order 243 Reviewed International coauthorship

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    J. Algebra   544   262 - 301   2020.2

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.jalgebra.2019.08.008

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  • Rationality problems for relation modules of dihedral groups Reviewed International coauthorship

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    J. Algebra   530   368 - 401   2019.7

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.jalgebra.2019.04.015

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  • Rationality Problem for Algebraic Tori Reviewed

    Akinari Hoshi, Aiichi Yamasaki

    MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY   248 ( 1176 )   1 - 215   2017.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER MATHEMATICAL SOC  

    We give the complete stably rational classification of algebraic tori of dimensions 4 and 5 over a field k. In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank 4 and 5 is given. We show that there exist exactly 487 (resp. 7, resp. 216) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 4, and there exist exactly 3051 (resp. 25, resp. 3003) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 5. We make a procedure to compute a flabby resolution of a G-lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a G-lattice is invertible (resp. zero) or not. Using the algorithms, we determine all the flabby and coflabby G-lattices of rank up to 6 and verify that they are stably permutation. We also show that the Krull-Schmidt theorem for G-lattices holds when the rank &lt;= 4, and fails when the rank is 5. Indeed, there exist exactly 11 (resp. 131) G-lattices of rank 5 (resp. 6) which are decomposable into two different ranks. Moreover, when the rank is 6, there exist exactly 18 G-lattices which are decomposable into the same ranks but the direct summands are not isomorphic. We confirm that H-1(G, F) = 0 for any Bravais group G of dimension n &lt;= 6 where F is the flabby class of the corresponding G-lattice of rank n. In particular, H-1(G, F) = 0 for any maximal finite subgroup G = GL(n, Z) where n &lt;= 6. As an application of the methods developed, some examples of not retract (stably) rational fields over k are given.

    DOI： 10.1090/memo/1176

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  • Complete solutions to a family of Thue equations of degree 12 Reviewed

    Akinari Hoshi

    JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX   29 ( 2 )   549 - 568   2017

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：UNIV BORDEAUX, INST MATHEMATIQUES BORDEAUX  

    We consider a parametric non-Galois family of Thue equations F-m(x, y) = lambda of degree 12 where m is an integral parameter and A is a divisor of 729(m(2) + 3m + 9). Using the field isomorphism method which is developed in [15], we show that the equations have only the trivial solutions with xy(x + y)(x - y) . (x + 2y)(2x + y) = 0.

    DOI： 10.5802/jtnb.991

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  • Degree three unramified cohomology groups Reviewed International coauthorship

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    JOURNAL OF ALGEBRA   458   120 - 133   2016.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let k be any field, G be a finite group. Let G act on the rational function field k(x(g) : g is an element of G) by k-automorphisms defined by h . x(g) = x(hg) for any g, h is an element of G. Denote by k(G) = k(x(g) : g is an element of G)(G), the fixed subfield. Noether's problem asks whether k(G) is rational (= purely transcendental) over k. The unramified Brauer group Br-nr(C(G)) and the unramified cohomology H-nr(3)(C(G), Q/Z) are obstructions to the rationality of C(G) (see [14] and [5]). Peyre proves that, if p is an odd prime number, then there is a group G such that vertical bar G vertical bar = p(12), Br-nr(C(G)) = {0}, but H-nr(3)(C(G), Q/Z) not equal {0}; thus C(G) is not stably C-rational [12]. Using Peyre's method, we are able to find groups G with vertical bar G vertical bar = p(9) where p is an odd prime number such that Br-nr(C(G)) = {0}, H-nr(3) (C(G), Q/Z) not equal {0}. (C) 2016 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jalgebra.2016.03.016

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  • Birational classification of fields of invariants for groups of order 128 Reviewed

    Akinari Hoshi

    JOURNAL OF ALGEBRA   445   394 - 432   2016.1

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let G be a finite group acting on the rational function field C(x(g) : g is an element of G) by C-automorphisms h(x(g)) = x(hg) for any g,h is an element of G. Noether's problem asks whether the invariant field C(G) = k(x(g) : g is an element of G)(G) is rational (i.e. purely transcendental) over C. By Fischer's theorem, C(G) is rational over C when G is a finite abelian group. Saltman and Bogomolov, respectively, showed that for any prime p there exist groups G of order p(9) and of order p(6) such that C(G) is not rational over C by showing the non-vanishing of the unraraified Brauer group: Bru(nr)(C(G)) not equal 0, which is an avatar of the birational invariant H-3 (X, Z)(tors) given by Artin and Mumford where X is a smooth projective complex variety whose function field is C(G). For p = 2, Chu, Hu, Kang and Prokhorov proved that if G is a 2-group of order &lt;= 32, then C(G) is rational over C. Chu, Hu, Kang and Kunyavskii showed that if G is of order 64, then C(G) is rational over C except for the groups G belonging to the two isoclinism families Phi(13) with Br-nr(C(G)) = 0 and Phi(16) with Br-nr(C(G)) similar or equal to C-2. Bogomolov and Bohning's theorem claims that if G(1) and G(2) belong to the same isoclinism family, then C(G(1)) and C(G(2)) are stably C-isomorphic. We investigate the birational classification of C(G) for groups G of order 128 with Br-nr(C(G)) not equal 0. Moravec showed that there exist exactly 220 groups G of order 128 with Br-nr(C(G)) not equal 0 forming 11 isoclinism families Phi(j). We show that if G(1) and G(2) belong to Phi(16), Phi(31), Phi(37), Phi(39), Phi(43), Phi(58), Phi(60) or Phi(80) (resp. Phi(106) or Phi(114)), then C(G(1)) and C(G(2)) are stably C-isomorphic with Br-nr(C(G(i))) similar or equal to C-2. Explicit structures of non-rational fields C(G) are given for each cases including also the case Phi(30) with Br-nr(C(G)) similar or equal to C-2 X C-2. (C) 2015 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jalgebra.2015.05.035

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  • Noether's problem for groups of order 243 Reviewed International coauthorship

    Huah Chu, Akinari Hoshi, Shou-Jen Hu, Ming-chang Kang

    JOURNAL OF ALGEBRA   442   233 - 259   2015.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let k be any field, G be a finite group. Let G act on the rational function field k(x(g) : g is an element of G) by k-automorphisms defined by h . x(g) = x(hg) for any g,h is an element of G. Denote by k(G) = k(x(g) : g is an element of G)(G) the fixed field. Noether's problem asks, under what situations, the fixed field k(G) will be rational (= purely transcendental) over k. According to the data base of GAP there are 10 isoclinism families for groups of order 243. It is known that there are precisely 3 groups G of order 243 (they consist of the isoclinism family Phi(10)) such that the unramified Brauer group of C(G) over C is non-trivial. Thus C(G) is not rational over C. We will prove that, if zeta(9) is an element of k, then k(G) is rational over k for groups of order 243 other than these 3 groups, except possibly for groups belonging to the isoclinism family Phi(7). (C) 2015 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jalgebra.2015.03.010

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  • On Noether's problem for cyclic groups of prime order Reviewed

    Akinari Hoshi

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   91 ( 3 )   39 - 44   2015.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：JAPAN ACAD  

    Let k be a field and G be a finite group acting on the rational function field k(x(g) vertical bar g is an element of G) by k-automorphisms h(x(g)) = x(hg) for any g, h is an element of G. Noether's problem asks whether the invariant field k(G) = k(x(g) vertical bar g is an element of G)(G) is rational (i.e. purely transcendental) over k. In 1974, Lenstra gave a necessary and sufficient condition to this problem for abelian groups G. However, even for the cyclic group C-p of prime order p, it is unknown whether there exist infinitely many primes p such that Q(C-p) is rational over Q. Only known 17 primes p for which Q(C-p) is rational over Q are p &lt;= 43 and p = 61,67,71. We show that for primes p &lt; 20000, Q(C-p) is not (stably) rational over Q except for affirmative 17 primes and undetermined 46 primes. Under the GRH, the generalized Riemann hypothesis, we also confirm that Q(C-p) is not (stably) rational over Q for undetermined 28 primes p out of 46.

    DOI： 10.3792/pjaa.91.39

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  • Rationality problem for quasi-monomial actions Reviewed

    Akinari Hoshi

    RIMS Kôkyûroku Bessatsu   B51   203 - 227   2014.10

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  • On the simplest quartic fields and related Thue equations Reviewed

    Akinari Hoshi

    Computer Mathematics   67 - 85   2014.10

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    Language：English   Publishing type：Research paper (international conference proceedings)  

    DOI： 10.1007/978-3-662-43799-5_7

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  • Quasi-monomial actions and some 4-dimensional rationality problems Reviewed International coauthorship

    Akinari Hoshi, Ming-chang Kang, Hidetaka Kitayama

    JOURNAL OF ALGEBRA   403   363 - 400   2014.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let G be a finite group acting on k(x(1), ..., x(n)), the rational function field of n variables over a field k. The action is called a purely monomial action if cr " xi = for all sigma is an element of G, for 1 &lt;= j &lt;= n where is an element of GL(n) (Z). The main question is that, under what situations, the fixed field k(x(1), ..., x(n))(G) is rational (= purely transcendental) over k. This rationality problem has been studied by Hajja, Kang, Hoshi, Rikuna when n 3. In this paper we will prove that k(x(1), x(2), x(3), x(4))(G) is rational over k provided that the purely monomial action is decomposable. To prove this result, we introduce a new notion, the quasi-monomial action, which is a generalization of previous notions of multiplicative group actions. Moreover, we determine the rationality problem of purely quasi-monomial actions of K(x, y)(G) over k where k = K-G. (C) 2014 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jalgebra.2014.01.019

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  • NOETHER'S PROBLEM AND UNRAMIFIED BRAUER GROUPS Reviewed International coauthorship

    Akinari Hoshi, Ming-Chang Kang, Boris E. Kunyavskii

    ASIAN JOURNAL OF MATHEMATICS   17 ( 4 )   689 - 713   2013.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：INT PRESS BOSTON, INC  

    Let k be any field, G be a finite group acting on the rational function field k(x(g) : g is an element of G) by h . x(g) = x(hg) for any h, g is an element of G. Define k(G) = k(x(g) : g is an element of G)(G). Noether's problem asks whether k(G) is rational (= purely transcendental) over k. It is known that, if C(G) is rational over C, then B-0(G) = 0 where B-0(G) is the unramified Brauer group of C(G) over C. Bogomolov showed that, if G is a p-group of order p(5), then B-0(G) = 0. This result was disproved by Moravec for p = 3, 5, 7 by computer calculations. We will prove the following theorem. Theorem. Let p be any odd prime number, G be a group of order p(5). Then B-0(G) not equal 0 if and only if G belongs to the isoclinism family Phi(10) in R. James's classification of groups of order p(5).

    DOI： 10.4310/AJM.2013.v17.n4.a8

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  • On the simplest sextic fields and related Thue equations Reviewed

    Akinari Hoshi

    Functiones et Approximatio Commentarii Mathematici   47 ( 1 )   35 - 49   2012.9

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    Publishing type：Research paper (scientific journal)   Publisher：Adam Mickiewicz University (Euclid)  

    DOI： 10.7169/facm/2012.47.1.3

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  • On correspondence between solutions of a family of cubic Thue equations and isomorphism classes of the simplest cubic fields Reviewed

    Akinari Hoshi

    JOURNAL OF NUMBER THEORY   131 ( 11 )   2135 - 2150   2011.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let m &gt;= -1 be an integer. We give a correspondence between integer solutions to the parametric family of cubic Thue equations
    X(3) - mX(2)Y - (m+3)XY(2) - Y(3) = lambda
    where lambda &gt; 0 is a divisor of m(2) + 3m + 9 and isomorphism classes of the simplest cubic fields. By the correspondence and R. Okazaki&apos;s result, we determine the exactly 66 non-trivial solutions to the Thue equations for positive divisors lambda of m(2) + 3m + 9. As a consequence, we obtain another proof of Okazaki&apos;s theorem which asserts that the simplest cubic fields are non-isomorphic to each other except for m = -1,0, 1, 2, 3, 5, 12, 54, 66, 1259, 2389. (C) 2011 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jnt.2011.05.001

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  • Rationality problem of three-dimensional monomial group actions Reviewed

    Akinari Hoshi, Hidetaka Kitayama, Aiichi Yamasaki

    JOURNAL OF ALGEBRA   341 ( 1 )   45 - 108   2011.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let K be a field of characteristic not two and K(x, y, z) the rational function field over K with three variables x, y. z. Let G be a finite group acting on K(x. y, z) by monomial K-automorphisms. We consider the rationality problem of the fixed field K(x, y, z)(G) under the action of G, namely whether K(x, y, z)(G) is rational (that is, purely transcendental) over K or not. We may assume that G is a subgroup of GL(3, Z) and the problem is determined up to conjugacy in GL(3, Z). There are 73 conjugacy classes of G in GL(3, Z). By results of Endo-Miyata, Voskresenskii, Lenstra, Saltman, Hajja. Rang and Yamasaki, 8 conjugacy classes of 2-groups in GL(3, Z) have negative answers to the problem under certain monomial actions over some base field K, and the necessary and sufficient condition for the rationality of K(x, y, z)(G) over K is given. In this paper, we show that the fixed field K (x. y,z)(G) under monomial action of G is rational over K except for possibly negative 8 cases of 2-groups and unknown one case of the alternating group of degree four. Moreover we give explicit transcendental bases of the fixed fields over K. For the unknown case, we obtain an affirmative solution to the problem under some conditions. In particular, we show that if K is quadratically closed field then K(x, y, z)(G) is rational over K. We also give an application of the result to 4-dimensional linear Noether&apos;s problem. (C) 2011 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jalgebra.2011.06.004

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  • TWISTED SYMMETRIC GROUP ACTIONS Reviewed International coauthorship

    Akinari Hoshi, Ming-chang Kang

    PACIFIC JOURNAL OF MATHEMATICS   248 ( 2 )   285 - 304   2010.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：PACIFIC JOURNAL MATHEMATICS  

    Let K be any field, let K (x(1),..., x(n)) be the rational function field of n variables over K, and let S-n and An be the symmetric group and the alternating group of degree n, respectively. For any a epsilon K\{0}, define an action of Sn on K (x(1),...,x(n)) by sigma center dot x(i) = x(sigma(i)) for sigma epsilon A(n) and sigma center dot x(i) = a/x(sigma(i)) for sigma epsilon S-n \ A(n). We prove that for any field K and n D 3; 4; 5, the fixed field K (x(1),...,x(n))(Sn) is rational (that is, purely transcendental) over K.

    DOI： 10.2140/pjm.2010.248.285

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  • ON THE FIELD INTERSECTION PROBLEM OF SOLVABLE QUINTIC GENERIC POLYNOMIALS Reviewed

    Akinari Hoshi, Katsuya Miyake

    INTERNATIONAL JOURNAL OF NUMBER THEORY   6 ( 5 )   1047 - 1081   2010.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

    We study a general method of the field intersection problem of generic polynomials over an arbitrary field k via formal Tschirnhausen transformation. In the case of solvable quintic, we give an explicit answer to the problem by using multi-resolvent polynomials.

    DOI： 10.1142/S179304211000337X

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  • A note on the field isomorphism problem of X^3+sX+s and related cubic Thue equations Reviewed

    Akinari Hoshi, Katsuya Miyake

    Interdiscip. Inform. Sci., Special Section: Japan-Korea Joint Seminar on Number Theory and Related Topics 2008   16 ( 1 )   45 - 54   2010.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Tohoku University  

    We study the field isomorphism problem of cubic generic polynomial <I>X</I><SUP>3</SUP>+<I>sX</I>+<I>s</I> over the field of rational numbers with the specialization of the parameter <I>s</I> to nonzero rational integers <I>m</I> via primitive solutions to the family of cubic Thue equations <I>x</I><SUP>3</SUP>−2<I>mx</I><SUP>2</SUP><I>y</I>−9<I>mxy</I><SUP>2</SUP>−<I>m</I>(2<I>m</I>+27)<I>y</I><SUP>3</SUP>=λ where λ<SUP>2</SUP> is a divisor of <I>m</I><SUP>3</SUP>(4<I>m</I>+27)<SUP>5</SUP>.

    DOI： 10.4036/iis.2010.45

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    Other Link： https://jlc.jst.go.jp/DN/JALC/00348817179?from=CiNii

  • SOME DIOPHANTINE PROBLEMS ARISING FROM THE ISOMORPHISM PROBLEM OF GENERIC POLYNOMIALS Reviewed

    Akinari Hoshi, Katsuya Miyake

    NUMBER THEORY: DREAMING IN DREAMS   6   87 - 105   2009.11

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

    Let k be a field and G a finite group. A k-generic polynomial for G covers all G-Galois extensions L/K over k by specializing parameters to elements of the bottom field K of the G-Galois extension. We study the field isomorphism problem of k-generic polynomials for various G's to determine the 'moduli' of G-Galois extensions given by them over K, and announce some results of cubic, quartic and quintic cases. In cubic and quartic cases over infinite field, we see that the generic polynomials give the same splitting fields for infinitely many specialized values of the parameters. For cubic generic polynomials with the least possible number of parameters, furthermore, we show by Siegel's Theorem for curves of genus 0 that there are only finitely many integral values of the parameters which may give the same number fields. We will also show a correspondence between integral solutions of some parametric cubic Thue equations and isomorphism classes of Shanks' simplest cubic fields. Some of the results of this survey article will be published elsewhere.

    DOI： 10.1142/9789814289924_0004

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  • On the field intersection problem of generic polynomials: a survey Reviewed

    Akinari Hoshi, Katsuya Miyake

    RIMS Kôkyûroku Bessatsu   B12   231 - 247   2009.8

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  • On the field intersection problem of quartic generic polynomials via formal Tschirnhausen transformation Reviewed

    Akinari Hoshi, Katsuya Miyake

    Comment. Math. Univ. St. Pauli   58 ( 1 )   51 - 86   2009.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Rikkyo University  

    DOI： 10.14992/00008648

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  • A geometric framework for the subfield problem of generic polynomials via Tschirnhausen transformation Reviewed

    Akinari Hoshi, Katsuya Miyake

    Number Theory and Applications: Proceedings of the International Conferences on Number Theory and Cryptography, Hindustan Book Agency   65 - 104   2009.3

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    DOI： 10.1007/978-93-86279-46-0

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  • A rationality problem of some Cremona transformation Reviewed International coauthorship

    Akinari Hoshi, Ming-chang Kang

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   84 ( 8 )   133 - 137   2008.10

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    In this note we give a new approach to the rationality problem of some, Cremona transformation. Let k be any field, k(x,y) be the rational function field of two variables over k. Let sigma be t k-automorphism of k(x,y) defined by
    sigma(x)= -x(3x-9y-y(2))(3)/(27x+2x(2)+9xy+2xy(2)-y(3))(2), sigma(y)=-(3x+y(2))(3x-9y-y(2))/27x+2x(2)+9xy+2xy(2)-y(3).
    Theorem. The fixed field k(x,y)((sigma)) is rational (= purely transcendental) over k. Embodied in a new proof of the above theorem several general guidelines for solving the rationality problem of Cremona transformations, which may be applied elsewhere.

    DOI： 10.3792/pjaa.84.133

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  • Rationality problem of three-dimensional purely monomial group actions: the last case Reviewed

    Akinari Hoshi, Yuichi Rikuna

    MATHEMATICS OF COMPUTATION   77 ( 263 )   1823 - 1829   2008.7

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    A k-automorphism sigma of the rational function field k(x(1), ... , x(n)) is called purely monomial if s sends every variable xi to a monic Laurent monomial in the variables x(1), ... , x(n). Let G be a finite subgroup of purely monomial k- automorphisms of k(x(1), ... , x(n)). The rationality problem of the G-action is the problem of whether the G- fixed field k( x(1), ... , x(n)) G is k- rational, i.e., purely transcendental over k, or not. In 1994, M. Hajja and M. Kang gave a positive answer for the rationality problem of the three-dimensional purely monomial group actions except one case. We show that the remaining case is also affirmative.

    DOI： 10.1090/S0025-5718-08-02069-3

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  • Noether's problem and $\mathbb{Q}$-generic polynomials for the normalizer of the 8-cycle in $S_8$ and its subgroups Reviewed

    Ki-ichiro Hashimoto, Akinari Hoshi, Yuichi Rikuna

    MATHEMATICS OF COMPUTATION   77 ( 262 )   1153 - 1183   2008.4

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    We study Noether's problem for various subgroups H of the normalizer of a group C-8 generated by an 8-cycle in S-8, the symmetric group of degree 8, in three aspects according to the way they act on rational function fields, i.e., Q(X-0 , . . . , X-7), Q(x(1) , . . . , x(4)), and Q(x, y). We prove that it has affirmative answers for those H containing C-8 properly and derive a Q-generic polynomial with four parameters for each H. On the other hand, it is known in connection to the negative answer to the same problem for C-8/Q that there does not exist a Q-generic polynomial for C-8. This leads us to the question whether and how one can describe, for a given field K of characteristic zero, the set of C-8-extensions L/K. One of the main results of this paper gives an answer to this question.

    DOI： 10.1090/S0025-5718-07-02094-7

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  • Tschirnhausen transformation of a cubic generic polynomial and a 2-dimensional involutive Cremona transformation Reviewed

    Akinari Hoshi, Katsuya Miyake

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   83 ( 3 )   21 - 26   2007.3

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    We study the field isomorphism problem for a cubic generic polynomial X-3 + sX + s via Tschirnhausen transformation. Through this process, there naturally appears a 2-dimensional involutive Cremona transformation. We show that the fixed field under the action of the transformation is purely transcendental over an arbitrary base field.

    DOI： 10.3792/pjaa.83.21

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  • Explicit lifts of quintic Jacobi sums and period polynomials $\mathbf{F}_q$ Reviewed

    Akinari Hoshi

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   82 ( 7 )   87 - 92   2006.9

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    DOI： 10.3792/pjaa.82.87

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  • Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations Reviewed

    Ki-ichiro Hashimoto, Akinari Hoshi

    MATHEMATICS OF COMPUTATION   74 ( 251 )   1519 - 1530   2005.7

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    A general method of constructing families of cyclic polynomials over Q with more than one parameter will be discussed, which may be called a geometric generalization of the Gaussian period relations. Using this, we obtain explicit multi-parametric families of cyclic polynomials over Q of degree 3 &lt;= e &lt;= 7. We also give a simple family of cyclic polynomials with one parameter in each case, by specializing our parameters.

    DOI： 10.1090/S0025-5718-05-01750-3

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  • Geometric generalization of gaussian period relations with application to noether’s problem for meta-cyclic groups Reviewed

    Ki-ichiro Hashimoto, Akinari Hoshi

    Tokyo Journal of Mathematics   28 ( 1 )   13 - 32   2005.6

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    We study Noether’s problem over Q for meta-cyclic groups. This paper is an extension of the previous work [2], which was concerned with the cyclic group Cn of order n. We shall give a simple description of the action of the normalizer of Cn in Sn to the function field Q(x1,…, xn), in terms of the generators of the fixed field of Cn given in [2]. Using this, we settle Noether’s problem for the dihedral group of order 2n (n ≤ 6) and the Frobenius group of order 20 with explicit construction of independent generators of the fixed fields. We shall also reconstruct some simple one-parameter families of cyclic and dihedral polynomials. © 2005 International Academic Printing Co. Ltd. All rights reserved.

    DOI： 10.3836/tjm/1244208276

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  • Noether's problem for some meta-abelian groups of small degree Reviewed

    Akinari Hoshi

    Proceedings of the Japan Academy Series A: Mathematical Sciences   81 ( 1 )   1 - 6   2005.1

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    In this note we solve Noether's problem over Q for some meta-abelian groups of small degree n. Let G be a subgroup of the group of one-dimensional affine transformations on Z/nZ which contains Z/nZ. For n = 9,10,12,14,15, we show that Noether's problem for G has an affirmative answer by constructing an explicit transcendental basis of the fixed field over Q.

    DOI： 10.3792/pjaa.81.1

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  • Multiplicative quadratic forms on algebraic varieties Reviewed

    Akinari Hoshi

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   79 ( 4 )   71 - 75   2003.4

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    In this note we extend Hurwitz-type multiplication of quadratic forms. For a regular quadratic space (K-n, q), we restrict the domain of q to an algebraic variety V subset of or equal to K-n and require a Hurwitz-type "bilinear condition" on V. This means the existence of a bilinear map phi: K-n x K-n --&gt; K-n such that phi(V x V) subset of V and q(X)q(Y) = q(phi(X, Y)) for any X, Y is an element of V. We show that the m-fold Pfister form is multiplicative on certain proper subvariety in K-2m for any m. We also show the existence of multiplicative quadratic forms which are different from Pfister forms on certain algebraic varieties for n = 4, 6. Especially for n = 4 we give a certain family of them.

    DOI： 10.3792/pjaa.79.71

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▶ display all

Books

  • 要点明解 線形数学 三訂版

    田中環, 小島秀雄, 星明考, 折田龍馬, 印南信宏, 吉原久夫（ Role： Joint author）

    培風館  2022.4  （ ISBN:9784563012410 ）

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  • An Introduction to Group Theory (Japanese)

    Akinari Hoshi（ Role： Sole author）

    NIPPON HYORON SHA CO.,LTD.  2016.3  （ ISBN:9784535788091 ）

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    Total pages：280   Language：Japanese Book type：Scholarly book

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  • 要点明解 線形数学 改訂版

    印南信宏, 田中環, 小島秀雄, 星明考（ Role： Joint author）

    培風館  2016.2  （ ISBN:9784563012007 ）

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Presentations

  • Hasse norm principle for $M_{11}$ extensions

    Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2023.3  Chuo University

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    Venue：Chuo University  

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  • Birational classification for algebraic tori (I)

    Akinari Hoshi, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2023.3  Chuo University

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    Venue：Chuo University  

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  • Birational classification for algebraic tori Invited

    Akinari Hoshi

    Yufuin Workshop on Algebraic Geometry (Prof. Masamichi Kuroda, Taketo Shirane, Kentaro Mitsui and Kazuhiko Yamaki)  2023.2  Nippon Bunri University

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    Venue：Nippon Bunri University  

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  • Hasse norm principle for $M_{11}$ extensions Invited

    Akinari Hoshi

    Niigata Algebra Seminar (Prof. Hideo Kojima and Takeshi Takahashi)  2022.11  Niigata Univ. + Zoom

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    Venue：Niigata Univ. + Zoom  

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  • Birational classification for algebraic tori (III) Invited

    Akinari Hoshi

    Niigata Algebra Seminar (Prof. Hideo Kojima and Takeshi Takahashi)  2022.5  Niigata Univ. + Zoom

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    Venue：Niigata Univ. + Zoom  

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  • Birational classification for algebraic tori (I) Invited

    Akinari Hoshi

    Niigata Algebra Seminar (Prof. Hideo Kojima and Takeshi Takahashi)  2022.4  Niigata Univ. + Zoom

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    Venue：Niigata Univ. + Zoom   Country：Japan  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Colloquium of Dept. of Math., Meijo Univ. (Prof. Yoshihiro Onishi and Tetsuya Uematsu)  2021.12  Zoom (Meijo)

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    Venue：Zoom (Meijo)  

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  • Davenport and Hasse's theorems and lifts of multiplication matrices of Gaussian periods

    Akinari Hoshi, Kazuki Kanai

    Autumn Meeting of the Mathematical Society of Japan  2021.9  Zoom (Chiba)

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    Venue：Zoom (Chiba)   Country：Japan  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Homotopic and Geometric Galois Theory, (Prof. Benjamin Collas, Pierre Debes, Hiroaki Nakamura and Jakob Stix)  2021.3  Zoom (Oberwolfach)

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    Venue：Zoom (Oberwolfach)  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Degenerations and models of algebraic varieties and related topics (Prof. Kentaro Mitsui, Ryo Ohkawa, Masa-Hiko Saito and Taro Sano)  2021.2  Zoom (Kobe)

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    Venue：Zoom (Kobe)  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    The 18th Symposium on Algebraic Curves (Prof. Akira Ohbuchi)  2020.12  Zoom (Tokushima)

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    Venue：Zoom (Tokushima)   Country：Japan  

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  • Norm one tori and Hasse norm principle

    Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2020.3  Nihon Univ.

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    Venue：Nihon Univ.   Country：Japan  

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  • Norm one tori and Hasse norm principle, II

    Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2020.3  Nihon University

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    Venue：Nihon University   Country：Japan  

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  • Degree three unramified cohomology groups and Noether's problem for groups of order 243 Invited

    Akinari Hoshi

    The 15th Polynomial Ring Theory Seminar (Prof. Shigeru Kuroda and Ryuji Tanimoto)  2020.2  Shizuoka Univ.

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    Venue：Shizuoka Univ.   Country：Japan  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    The 41st Symposium on Commutative Algebra (Prof. Tokuji Araya, Mitsuyasu Hashimoto and Futoshi Hayasaka)  2019.11  Kurashiki Seaside Hotel

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    Venue：Kurashiki Seaside Hotel   Country：Japan  

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  • Norm one tori and Hasse norm principle (III) Invited

    Akinari Hoshi

    Niigata Algebra Seminar (Prof. Hideo Kojima and Takeshi Takahashi)  2019.11  Niigata Univ.

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    Venue：Niigata Univ.   Country：Japan  

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  • Degree three unramified cohomology groups and Noether's problem for groups of order 243 Invited

    Akinari Hoshi

    Geometry of Projective Varieties and Related Topics 2019 (Prof. Yoshiaki Fukuma, Hideo Kojima and Takeshi Harui)  2019.11  Kochi Univ.

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    Venue：Kochi Univ.   Country：Japan  

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  • Norm one tori and Hasse norm principle (II) Invited

    Akinari Hoshi

    Niigata Algebra Seminar (Prof. Hideo Kojima and Takeshi Takahashi)  2019.10  Niigata Univ.

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    Venue：Niigata Univ.   Country：Japan  

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  • Degree three unramified cohomology groups and Noether's problem Invited

    Akinari Hoshi

    The 27th Summer School on Number Theory (Prof. Toru Komatsu and Hidetaka Kitayama)  2019.9  Tohoku University of Community Service and Science

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    Venue：Tohoku University of Community Service and Science  

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  • Quasi-monomial actions and rationality problem Invited

    Akinari Hoshi

    The 27th Summer School on Number Theory (Prof. Toru Komatsu and Hidetaka Kitayama)  2019.9  Tohoku University of Community Service and Science

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    Venue：Tohoku University of Community Service and Science  

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  • Degree three unramified cohomology groups and Noether's problem for groups of order 243 Invited

    Akinari Hoshi

    NCTS Seminar on Algebra (Prof. Ming-chang Kang)  2019.8  National Taiwan Univ.

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    Venue：National Taiwan Univ.   Country：Taiwan, Province of China  

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  • Degree three unramified cohomology groups and Noether's problem for groups of order 243 Invited

    Akinari Hoshi

    Conference: Commutative Banach Algebra and Related Topics (Prof. Takeshi Miura and Takahiro Hayata)  2019.6  Yamagata Univ.

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    Venue：Yamagata Univ.   Country：Japan  

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  • Rationality problem for algebraic tori Invited

    Akinari Hoshi

    Niigata Algebra Seminar (Prof. Hideo Kojima and Takeshi Takahashi)  2019.6  Niigata Univ.

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    Venue：Niigata Univ.   Country：Japan  

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  • Rationality problem for norm one tori, II

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2019.3  Tokyo Institute of Technology

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    Venue：Tokyo Institute of Technology   Country：Japan  

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  • Noether's problem for $N\rtimes A_6$

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2019.3  Tokyo Institute of Technology

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    Venue：Tokyo Institute of Technology   Country：Japan  

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  • Rationality problem for norm one tori

    Akinari Hoshi, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2019.3  Tokyo Institute of Technology

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    Venue：Tokyo Institute of Technology   Country：Japan  

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  • Degree three unramified cohomology groups and Noether's problem for groups of order 243 Invited

    Akinari Hoshi

    Seminaire "Varietes Rationnelles" (Prof. Jean-Louis Colliot-Thelene, Cyril Demarche and Mathieu Florence)  2018.6  Universite Pierre-et-Marie-Curie (Paris VI)

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    Venue：Universite Pierre-et-Marie-Curie (Paris VI)   Country：France  

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  • Rationality problem for fields of invariants and unramified cohomology groups Invited

    Akinari Hoshi

    International Workshop on Algebra (Prof. Jungkai Alfred Chen and Chia-Fu Yu)  2018.6  National Taiwan Univ.

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    Venue：National Taiwan Univ.   Country：Taiwan, Province of China  

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  • Degree three unramified cohomology groups and Noether's problem for groups of order 243 (II) Invited

    Akinari Hoshi

    Niigata Algebra Seminar (Prof. Hideo Kojima and Takeshi Takahashi)  2018.5  Niigata Univ.

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    Venue：Niigata Univ.  

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  • Computation of degree three unramified cohomology groups using GAP

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2018.3  The University of Tokyo

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    Venue：The University of Tokyo  

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  • Degree three unramified cohomology groups and Noether's problem for groups of order 243

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2018.3  The University of Tokyo

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    Venue：The University of Tokyo  

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  • Degree three unramified cohomology groups and Noether's problem for groups of order 243 Invited

    Akinari Hoshi

    Niigata Algebra Seminar (Prof. Hideo Kojima and Takeshi Takahashi)  2017.12  Niigata Univ.

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    Venue：Niigata Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Kinosaki algebraic geometry symposium 2017 (Prof. Taro Fujisawa, Takuzo Okada and Taro Sano)  2017.10  Kinosaki International Arts Center

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    Venue：Kinosaki International Arts Center  

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  • Unramified Brauer group of multiplicative invariant fields of dimension $\le 6$ (I) Invited

    Akinari Hoshi

    NCTS Seminar on Algebra (Prof. Ming-chang Kang)  2017.9  National Taiwan Univ.

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    Venue：National Taiwan Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Kagurazaka Algebra Seminar (Prof. Masanari Kida)  2017.7  Tokyo University of Science

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    Venue：Tokyo University of Science  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Algebra Seminar (Prof. Masanobu Kaneko, Shinichi Kobayashi and Shun'ichi Yokoyama)  2017.7  Kyushu Univ.

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    Venue：Kyushu Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Conference: Commutative Banach Algebra and Related Topics (Prof. Takeshi Miura and Takahiro Hayata)  2017.7  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • Cubic Thue equations and simplest cubic fields Invited

    Akinari Hoshi

    Journees Algophantiennes Bordelaises 2018 (Prof. Yuri Bilu)  2017.6  Universite Bordeaux

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    Venue：Universite Bordeaux  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Algebraic Geometry Seminar (Prof. Takehiko Yasuda)  2017.5  Osaka Univ.

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    Venue：Osaka Univ.  

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  • Multiplicative invariant fields of dimension $n \le 6$

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2017.3  Tokyo Metropolitan Univ.

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    Venue：Tokyo Metropolitan Univ.  

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  • Relation modules of dihedral groups

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2017.3  Tokyo Metropolitan Univ.

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    Venue：Tokyo Metropolitan Univ.  

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  • Degree three unramifed cohomology groups (II)

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2017.3  Tokyo Metropolitan Univ.

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    Venue：Tokyo Metropolitan Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    The 15th Affine Algebraic Geometry Meeting (Prof. Hideo Kojima, Takashi Kishimoto, Adrien Dubouloz and Kayo Masuda)  2017.3  Kwansei Gakuin Univ.

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    Venue：Kwansei Gakuin Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Niigata Algebra Seminar (Prof. Hideo Kojima and Takeshi Takahashi)  2016.12  Niigata Univ.

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    Venue：Niigata Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Workshop: Algebraic Number Theory and Related Topics (Prof. Yasuo Ohno and Hiroshi Tsunogai)  2016.11  Kyoto Univ.

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    Venue：Kyoto Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Workshop: Researches on isometries from various viewpoints (Prof. Takeshi Miura)  2016.10  Kyoto Univ.

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    Venue：Kyoto Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Japan-Taiwan Joint conference on Number theory 2017 (Prof. Ming-Lun Hsieh and Masataka Chida)  2016.9  National Taiwan Univ.

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    Venue：National Taiwan Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Matsue Seminar (Prof. Miho Aoki)  2016.7  Shimane Univ.

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    Venue：Shimane Univ.  

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  • On the simplest cubic fields and related Thue equations Invited

    Akinari Hoshi

    Matsue Seminar (Prof. Miho Aoki)  2016.7  Shimane Univ.

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    Venue：Shimane Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Workshop: Rationality and selfmaps of algebraic varieties (Prof. Shigeru Mukai and Keiji Oguiso)  2016.7  Kyoto Univ.

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    Venue：Kyoto Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Aichi Number Theory Seminar (Prof. Yasuhiro Kishi and Yasushi Mizusawa)  2016.7  Aichi Institute of Technology, Motoyama Campus

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    Venue：Aichi Institute of Technology, Motoyama Campus  

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  • On the simplest cubic fields and related Thue equations Invited

    Akinari Hoshi

    Conference: Commutative Banach Algebra and Related Topics (Prof. Takeshi Miura and Takahiro Hayata)  2016.7  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • Birational classification of fields of invariants for groups of order 128 Invited

    Akinari Hoshi

    Workshop on Galois point and related topics (Prof. Kei Miura, Takeshi Takahashi and Satoru Fukasawa)  2016.6  Niigata Univ., Satellite campus

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    Venue：Niigata Univ., Satellite campus  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Colloquium of Dept. of Math.  2016.5  Tokyo University of Science

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    Venue：Tokyo University of Science  

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  • Three-dimensional purely quasi-monomial actions

    Akinari Hoshi, Hidetaka Kitayama

    Spring Meeting of the Mathematical Society of Japan  2016.3  Tsukuba Univ.

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    Venue：Tsukuba Univ.  

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  • Degree three unramified cohomology groups

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2016.3  Tsukuba Univ.

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    Venue：Tsukuba Univ.  

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  • Bravais group of dimension $n \le 6$ and corresponding quadratic forms

    Akinari Hoshi, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2016.3  Tsukuba Univ.

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    Venue：Tsukuba Univ.  

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  • On Noether's problem for cyclic groups of prime order

    Akinari Hoshi

    Spring Meeting of the Mathematical Society of Japan  2016.3  Tsukuba Univ.

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    Venue：Tsukuba Univ.  

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  • On the simplest number fields and related Thue equations Invited

    Akinari Hoshi

    Analytic Number Theory Seminar (Prof. Koji Matsumoto)  2015.12  Nagoya Univ.

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    Venue：Nagoya Univ.  

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  • Birational classification of fields of invariants for groups of order 128 Invited

    Akinari Hoshi

    The 11th workshop on algebraic surfaces at Akihabara (Prof. Kazuhiro Konno and Hiro-o Tokunaga)  2015.10  Tokyo Metropolitan Univ., Akihabara Satellite Campus

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    Venue：Tokyo Metropolitan Univ., Akihabara Satellite Campus  

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  • On Noether's problem for cyclic groups of prime order Invited

    Akinari Hoshi

    Wokshop: Towards new development of mathematics via computational algebra system (Prof. Shun'ichi Yokoyama, Manabu Oura, Masanari Kida and Akihiro Munemasa)  2015.9  Kyoto Univ.

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    Venue：Kyoto Univ.  

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  • On the simplest number fields and related Thue equations Invited

    Akinari Hoshi

    The 4th International Congress on Natural Sciences (ICNS2016)  2015.9  National Changhua Univ. of Education

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    Venue：National Changhua Univ. of Education  

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  • On the simplest number fields and related Thue equations Invited

    Akinari Hoshi

    30th Journees Arithmetiques (JA2015)  2015.9  Univ. of Debrecen

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    Venue：Univ. of Debrecen  

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  • Rationality problem for algebraic tori Invited

    Akinari Hoshi

    Conference: Commutative Banach Algebra and Related Topics (Prof. Takeshi Miura and Takahiro Hayata)  2015.6  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • Birational classification of fields of invariants for groups of order 128

    Akinari Hoshi

    Spring Meeting of the Mathematical Society of Japan  2015.3  Meiji Univ.

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    Venue：Meiji Univ.  

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  • On the simplest cubic fields and related Thue equations Invited

    Akinari Hoshi

    Joint Seminar and Reseach Camp (JSRC2016)  2015.3  Niigata Univ.

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    Venue：Niigata Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    New Developments in Algebraic Geometry (Prof. Yoshiaki Fukuma and Hideo Kojima)  2014.11  Kochi Univ.

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    Venue：Kochi Univ.  

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  • Birational classification of fields of invariants for groups of order 128 Invited

    Akinari Hoshi

    New Developments in Algebraic Geometry (Prof. Caucher Birkar, Jungkai Alfred Chen, Wu-Yen Chuang and Jeng-Daw Yu)  2014.9  National Taiwan Univ.

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    Venue：National Taiwan Univ.  

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  • Rationality problem for algebraic tori

    Akinari Hoshi, Aiichi Yamasaki

    SEOUL ICM 2015  2014.8  Coex

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    Venue：Coex  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Conference: Commutative Banach Algebra and Related Topics (Prof. Takeshi Miura and Takahiro Hayata)  2014.6  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • Class numbers and algebraic tori

    Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2014.3  Gakushuin Univ.

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    Venue：Gakushuin Univ.  

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  • Rationality problem for fields of invariants Invited

    Akinari Hoshi

    Workshop on Galois point and related topics (Prof. Kei Miura, Takeshi Takahashi and Satoru Fukasawa),  2013.9  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • Noether's problem and unramified Brauer groups Invited

    Akinari Hoshi

    Nishi-Waseda Seminar on Number Theory (Prof. Yumiko Hironaka)  2013.9  Waseda Univ.

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    Venue：Waseda Univ.  

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  • Rationality problem for fields of invariants: a survey Invited

    Akinari Hoshi, Aiichi Yamasaki

    One-day workshop of algebra (Prof. Ming-chang Kang)  2013.8  National Taiwan Univ.

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    Venue：National Taiwan Univ.  

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  • Noether's problem and unramified Brauer groups (joint work with M. Kang and B.E. Kunyavskii) Invited

    Akinari Hoshi

    Algebraic Geometry Seminar (Prof. Shigeyuki Kondo and Shohei Ma)  2013.6  Nagoya Univ.

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    Venue：Nagoya Univ.  

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  • Krull-Schmidt theorem fails for dimension 5

    Akinari Hoshi, Aiichi Yamasaki

    Spring Meeting of the Mathematical Society of Japan  2013.3  Kyoto Univ.

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    Venue：Kyoto Univ.  

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  • Rationality problem for fields of invariants --from the viewpoint of inverse Galois problem-- Invited

    Akinari Hoshi

    Colloquium of Dept. of Math.  2013.1  Rikkyo Univ.

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    Venue：Rikkyo Univ.  

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  • Rationality problem of quasi-monomial actions Invited

    Akinari Hoshi

    Workshop: Algebraic Number Theory and Related Topics (Prof. Atsushi Shiho and Tadashi Ochiai)  2012.12  Kyoto Univ.

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    Venue：Kyoto Univ.  

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  • Rationality problem for fields of invariants --from the viewpoint of inverse Galois problem-- Invited

    Akinari Hoshi

    Joint seminar: The 108th 7th-Floor Seminar (Colloquium)  2012.11  Waseda Univ.

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    Venue：Waseda Univ.  

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  • Rationality problem for algebraic tori

    Akinari Hoshi, Aiichi Yamasaki

    Autumn Meeting of the Mathematical Society of Japan  2012.9  Kyushu Univ.

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    Venue：Kyushu Univ.  

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  • Noether's problem and unramified Brauer groups

    Akinari Hoshi, Ming-chang Kang, Boris E. Kunyavskii

    Autumn Meeting of the Mathematical Society of Japan  2012.9  Kyushu Univ.

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    Venue：Kyushu Univ.  

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  • Noether's problem and unramified Brauer groups (joint work with M. Kang and B.E. Kunyavskii) Invited

    Akinari Hoshi

    Workshop on Galois point and related topics (Prof. Kei Miura, Takeshi Takahashi and Satoru Fukasawa)  2012.9  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • Rationality problem of algebraic tori (I) (joint work with A. Yamasaki) Invited

    Akinari Hoshi

    One-day workshop of algebra (Prof. Ming-chang Kang)  2012.8  National Taiwan Univ.

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    Venue：National Taiwan Univ.  

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  • Noether's problem and unramified Brauer groups (joint work with M. Kang and B.E. Kunyavskii) Invited

    Akinari Hoshi

    The 7th Fukuoka Number Theory Conference (Prof. Masanobu Kaneko, Yasuro Gon and Yasuhiro Kishi)  2012.8  Kyushu Univ.

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    Venue：Kyushu Univ.  

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  • On the simplest cubic fields and related Thue equations Invited

    Akinari Hoshi

    The 2nd conference on MAGMA (Prof. Manabu Oura, Masanari Kida, Masaaki Harada, Akihiro Munemasa and Shun'ichi Yokoyama)  2012.7  Kochi Univ.

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    Venue：Kochi Univ.  

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  • Noether's problem and unramified Brauer groups (joint work with M. Kang and B.E. Kunyavskii) Invited

    Akinari Hoshi

    The 11th conference of Sendai-Hiroshima number theory (Prof. Toshiro Hiranouchi, Makoto Matsumoto, Hiroki Sumida-Takahashi, Nobuo Tsuzuki and Akihiko Yukie)  2012.7  Tohoku Univ.

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    Venue：Tohoku Univ.  

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  • Noether's problem and unramified Brauer groups (joint work with M. Kang and B.E. Kunyavskii) Invited

    Akinari Hoshi

    Conference: Commutative Banach Algebra and Related Topics (Prof. Sin-Ei Takahasi and Takeshi Miura)  2012.6  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • Noether's problem and unramified Brauer groups (joint work with M. Kang and B.E. Kunyavskii) Invited

    Akinari Hoshi

    Singularity Theory Monday Seminar (Prof. Kei-Ichi Watanabe)  2012.5  Nihon Univ.

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    Venue：Nihon Univ.  

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  • Quasi-monomial actions and some 4-dimensional rationality problems

    Akinari Hoshi, Ming-chang Kang, Hidetaka Kitayama

    Spring Meeting of the Mathematical Society of Japan  2012.3  Tokyo Univ. of Science

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    Venue：Tokyo Univ. of Science  

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  • Unramified Brauer groups for groups of order $p^5$

    Akinari Hoshi, Ming-chang Kang

    Spring Meeting of the Mathematical Society of Japan  2012.3  Tokyo Univ. of Science

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    Venue：Tokyo Univ. of Science  

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  • Unramified Brauer groups for groups of order $p^5$ (joint work with M. Kang and B.E. Kunyavskii) Invited

    Akinari Hoshi

    Mini-Conference on Algebraic Geometry (Prof. Fumio Sakai)  2012.3  Saitama Univ.

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    Venue：Saitama Univ.  

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  • Quasi-monomial actions and some 4-dimensional rationality problems (joint work with M. Kang and H. Kitayama) Invited

    Akinari Hoshi

    The 9th Affine Algebraic Geometry Meeting (Prof. Takashi Kishimoto, Hideo Kojima and Shigeru Kuroda)  2012.3  Kwansei Gakuin Univ.

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    Venue：Kwansei Gakuin Univ.  

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  • On the simplest cubic fields and related Thue equations Invited

    Akinari Hoshi

    Colloquium of Dept. of Math.  2012.1  Rikkyo Univ.

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    Venue：Rikkyo Univ.  

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  • On the simplest sextic fields and related Thue equations Invited

    Akinari Hoshi

    One-day workshop of algebra (Prof. Ming-chang Kang)  2011.8  National Taiwan Univ.

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    Venue：National Taiwan Univ.  

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  • Three-dimensional monomial group actions (joint work with H. Kitayama and A. Yamasaki) Invited

    Akinari Hoshi

    Seminar of Algebra (Prof. Ming-chang Kang)  2010.10  National Taiwan Univ.

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    Venue：National Taiwan Univ.  

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  • Three-dimensional monomial group actions (joint work with H. Kitayama and A. Yamasaki) Invited

    Akinari Hoshi

    TIMS Lecture (Prof. Ming-chang Kang)  2010.10  National Taiwan Univ.

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    Venue：National Taiwan Univ.  

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  • On the simplest sextic fields and related Thue equations

    Akinari Hoshi

    Autumn Meeting of the Mathematical Society of Japan  2010.9  Nagoya Univ.

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    Venue：Nagoya Univ.  

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  • On the simplest cubic fields and related Thue equations

    Akinari Hoshi

    Autumn Meeting of the Mathematical Society of Japan  2010.9  Nagoya Univ.

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    Venue：Nagoya Univ.  

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  • Rationality problem of twisted symmetric group actions

    Akinari Hoshi

    Spring Meeting of the Mathematical Society of Japan  2010.3  Keio Univ.

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    Venue：Keio Univ.  

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  • Rationality problem of three-dimensional monomial group actions (joint work with H. Kitayama and A. Yamasaki) Invited

    Akinari Hoshi

    The 5th Affine Algebraic Geometry Meeting (Prof. Kayo Masuda, Hideo Kojima and Takashi Kishimoto)  2010.3  Kwansei Gakuin Univ.

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    Venue：Kwansei Gakuin Univ.  

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  • Rationality problem for three-dimensional monomial group actions Invited

    Akinari Hoshi, Hidetaka Kitayama, Aiichi Yamasaki

    Joint Conference: Hokuriku Number Theory Conference and Galois theory and related topics (Prof. Ki-ichiro Hashimoto and Akito Nomura)  2009.12  Kanazawa Univ.

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    Venue：Kanazawa Univ.  

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  • Simple families of cyclic polynomials and related problems Invited

    Akinari Hoshi

    Joint Conference: Hokuriku Number Theory Conference and Galois theory and related topics (Prof. Ki-ichiro Hashimoto and Akito Nomura)  2009.12  Kanazawa Univ.

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    Venue：Kanazawa Univ.  

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  • On the simplest quartic fields and related Thue equations Invited

    Akinari Hoshi

    The Joint Conference of ASCM2009 and MACIS2010 (Prof. Guenael Renault and Kazuhiro Yokoyama)  2009.12  JAL Resort Sea Hawk Hotel Fukuoka

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    Venue：JAL Resort Sea Hawk Hotel Fukuoka  

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  • Three-dimensional monomial group actions

    Akinari Hoshi, Hidetaka Kitayama, Aiichi Yamasaki

    Autumn Meeting of the Mathematical Society of Japan  2009.9  Osaka Univ.

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    Venue：Osaka Univ.  

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  • On the field isomorphism problem of $X^3+sX+s$ and related cubic Thue equations

    Akinari Hoshi, Katsuya Miyake

    Autumn Meeting of the Mathematical Society of Japan  2009.9  Osaka Univ.

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    Venue：Osaka Univ.  

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  • On correspondence between solutions of a parametric family of cubic Thue equations and isomorphism classes of simplest cubic fields Invited

    Akinari Hoshi

    Conference: Diophantine Analysis and Related Fields 2009 (Prof. Noriko Hirata-Kohno, Masaaki Amou, Ryotaro Okazaki, Takao Komatsu and Isao Wakabayashi)  2009.3  Nihon Univ.

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    Venue：Nihon Univ.  

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  • On the field isomorphism problem of generic polynomials via formal Tschirnhausen transformation Invited

    Akinari Hoshi, Katsuya Miyake

    The Japan-Korea Joint Seminar on Number Theory and Related Topics 2008 (Prof. Hisao Taya)  2008.11  Tohoku Univ.

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    Venue：Tohoku Univ.  

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  • Note on the field isomorphism problem of generic polynomials

    Akinari Hoshi, Katsuya Miyake

    Autumn Meeting of the Mathematical Society of Japan  2008.9  Tokyo Institute of Technology

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    Venue：Tokyo Institute of Technology  

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  • On the field isomorphism problem of generic polynomials via formal Tschirnhausen transformation Invited

    Akinari Hoshi, Katsuya Miyake

    Conference: Galois theory and related topics (Prof. Ki-ichiro Hashimoto, Shin-ichi Katayama, Hiroaki Nakamura, Hiroki Sumida-Takahashi and Masanari Kida)  2008.9  Tokushima Univ.

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    Venue：Tokushima Univ.  

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  • Some Diophantine problems arising from the isomorphism problem of generic polynomials Invited

    Akinari Hoshi, Katsuya Miyake

    The 5th Japan-China Seminar on Number Theory (Prof. Shigeru Kanemitsu)  2008.8  Kinki Univ.

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    Venue：Kinki Univ.  

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  • Note on the field intersection problem of generic polynomials Invited

    Akinari Hoshi

    Conference: Commutative Banach Algebra and Related Topics (Prof. Sin-Ei Takahasi and Takeshi Miura)  2008.7  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • On the field intersection problem of generic polynomials via resolvent polynomials Invited

    Akinari Hoshi

    Foundations of Computational Mathematics (FoCM'09) (Prof. Hendrik Lenstra, Takakazu Satoh and Peter Stevenhagen)  2008.6  City Univ. of Hong Kong

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    Venue：City Univ. of Hong Kong  

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  • A geometric framework for the subfield problem of generic polynomials via Tschirnhausen transformation (joint work with K. Miyake) Invited

    Akinari Hoshi

    Conference: Algebraic Number Theory and Related Topics (Prof. Mamoru Asada and Hiroaki Nakamura)  2007.12  Kyoto Univ.

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    Venue：Kyoto Univ.  

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  • Note on the field isomorphism problem of generic polynomials (joint work with K. Miyake) Invited

    Akinari Hoshi

    The 7th Symposium on Algebra and Computation (AC2007) (Prof. Ken Nakamula, Michio Ozeki, Nobuki Takayama, Katsushi Waki, Hirofumi Tsumura and Shigenori Uchiyama)  2007.12  Tokyo Metropolitan Univ.

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    Venue：Tokyo Metropolitan Univ.  

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  • A geometric framework for the subfield problem of generic polynomials via Tschirnhausen transformation Invited

    Akinari Hoshi, Katsuya Miyake

    Conference: Galois theory and related topics (Prof. Ki-ichiro Hashimoto, Naoki Murabayashi and Masanari Kida)  2007.11  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • A geometric framework for the subfield problem of generic polynomials via Tschirnhausen transformation (joint work with K. Miyake) Invited

    Akinari Hoshi

    Number Theory Seminar at Waseda Univ. (Prof. Ki-ichiro Hashimoto and Keiichi Komatsu)  2007.10  Waseda Univ.

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    Venue：Waseda Univ.  

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  • Cubic generic polynomials and some Cremona transformations (joint work with Prof. K. Miyake) Invited

    Akinari Hoshi

    Seminar of Algebra (Prof. Ming-chang Kang)  2007.7  National Taiwan Univ.

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    Venue：National Taiwan Univ.  

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  • On Tschirnhausen transformations and the field isomorphism problem of cubic generic polynomials Invited

    Akinari Hoshi

    Conference: Commutative Banach Algebra and Related Topics (Prof. Sin-Ei Takahasi and Takeshi Miura)  2007.7  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • Constructive Study in Inverse Galois Problem (Survey Talk) -Generic polynomial and Noether's problem- Invited

    Akinari Hoshi

    Workshop on Galois point and related topics (Prof. Masaaki Homma and Hisao Yoshihara)  2007.7  Kanagawa Univ. Fujimi-kogen kenshujyo

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    Venue：Kanagawa Univ. Fujimi-kogen kenshujyo  

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  • Tschirnhausen transformation of a cubic generic polynomial and a 2-dimensional involutive Cremona transformation Invited

    Akinari Hoshi

    NCTS Short Course on Number Theory (Prof. Wen-Ching Winnie Li and Jing Yu)  2007.6  National Tsing Hua Univ.

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    Venue：National Tsing Hua Univ.  

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  • Tschirnhausen Transformation of a Cubic Generic Polynomial and a 2-dimensional Involutive Cremona Transformation Invited

    Akinari Hoshi, Katsuya Miyake

    International Conference on Number Theory (Prof. Balakrishnan Ramakrishnan and Kalyan Chakraborty)  2006.12  Harish-Chandra Research Institute

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    Venue：Harish-Chandra Research Institute  

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  • An involution of the Cremona group derived from Tschirnhausen transformations of generic cubic polynomials and the rationality of its fixed field

    Akinari Hoshi, Katsuya Miyake

    Autumn Meeting of the Mathematical Society of Japan  2006.9  Osaka City Univ.

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    Venue：Osaka City Univ.  

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  • An involution of the Cremona group derived from Tschirnhausen transformations of generic cubic polynomials and the rationality of its fixed field Invited

    Akinari Hoshi

    The 1st Fukuoka Number Theory Conference (Prof. Toru Komatsu)  2006.8  Kyushu Univ.

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    Venue：Kyushu Univ.  

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  • Noether's problem and generic polynomial -from the view point of Inverse Galois Problem- Invited

    Akinari Hoshi

    Conference: Commutative Banach Algebra and Related Topics (Prof. Sin-Ei Takahasi and Takeshi Miura)  2006.7  Yamagata Univ.

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    Venue：Yamagata Univ.  

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  • Generic Polynomials in Inverse Galois Problem (Survey Talk) Invited

    Akinari Hoshi

    The 69th 7th-Floor Seminar (Colloquium)  2006.6  Waseda Univ.

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    Venue：Waseda Univ.  

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  • Noether's problem for Frobenius groups of prime degree up to 23 Invited

    Akinari Hoshi

    Conference: Galois groups and algebraic equations (Prof. Ki-ichiro Hashimoto, Masanari Kida and Nobuhiro Terai)  2005.9  Kagoshima Univ.

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    Venue：Kagoshima Univ.  

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  • Noether's problem and Q-generic polynomials for the normalizer of the 8-cycle in $S_8$ and its subgroups Invited

    Akinari Hoshi

    Vortrag in der Arbeitsgemeinschaft ueber Algebra (Prof. Gregor Kemper)  2005.7  Technische Universitaet Muenchen

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    Venue：Technische Universitaet Muenchen  

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  • Noether Problems and Q-Generic Polynomials for the Normalizer of the 8-Cycle in $S_8$ Invited

    Akinari Hoshi

    Oberseminar Algebra-Zahlentheorie (Prof. B. Heinrich Matzat)  2005.5  Ruprecht-Karls-Universitaet Heidelberg

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    Venue：Ruprecht-Karls-Universitaet Heidelberg  

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  • Noether's problem and Q-generic polynomials Invited

    Akinari Hoshi

    Kolloquium in Universitaet des Saarlandes (Prof. Rainer Schulze-Pillot)  2005.5  Universitaet des Saarlandes

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    Venue：Universitaet des Saarlandes  

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  • Explicit construction of some multiplicative quadratic forms on algebraic varieties Invited

    Akinari Hoshi

    Oberseminar ueber Reelle Algebra (Prof. Manfred Knebusch)  2005.4  Universitaet Regensburg

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    Venue：Universitaet Regensburg  

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  • A remark on rational bioctic reciprocity law Invited

    Akinari Hoshi

    Oberseminar ueber Reelle Algebra (Prof. Manfred Knebusch)  2004.11  Universitaet Regensburg

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    Venue：Universitaet Regensburg  

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  • Multiplicative quadratic forms on algebraic varieties II Invited

    Akinari Hoshi

    Oberseminar ueber Reelle Algebra (Prof. Manfred Knebusch)  2004.11  Universitaet Regensburg

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    Venue：Universitaet Regensburg  

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  • Multiplicative quadratic forms on algebraic varieties Invited

    Akinari Hoshi

    Oberseminar ueber Reelle Algebra (Prof. Manfred Knebusch)  2004.11  Universitaet Regensburg

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    Venue：Universitaet Regensburg  

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  • Noether's Problem for meta-abelian groups Invited

    Akinari Hoshi

    Number Theory Seminar at Tokyo Metropolitan Univ. (Prof. Toru Komatsu and Yuichi Rikuna)  2004.4  Tokyo Metropolitan Univ.

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    Venue：Tokyo Metropolitan Univ.  

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  • Noether's Problem for Frobenius groups of degree 7 and its generic dimension

    Akinari Hoshi

    Spring Meeting of the Mathematical Society of Japan  2004.3  Tsukuba Univ.

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    Venue：Tsukuba Univ.  

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  • Noether's Problem for meta-abelian groups Invited

    Akinari Hoshi

    Workshop on Number Theory at Waseda Univ. (Prof. Ki-ichiro Hashimoto and Keiichi Komatsu)  2004.3  Waseda Univ.

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    Venue：Waseda Univ.  

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  • On the structure of the C8-fixed field of Q(x1，...，x8) Invited

    Akinari Hoshi

    Workshop: Inverse Galois Problem and Galois Coverings III (Prof. Hirotada Naito, Hiroki Sumida-Takahashi and Hiro-o Tokunaga)  2004.1  Kagawa Univ.

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    Venue：Kagawa Univ.  

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  • Geometric generalization of Gaussian period relations with application to Noether's problem for meta-cyclic groups

    Ki-ichiro Hashimoto, Akinari Hoshi

    Autumn Meeting of the Mathematical Society of Japan  2003.9  Chiba Univ.

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    Venue：Chiba Univ.  

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  • Noether's Problem for D5， F20 and D6 Invited

    Akinari Hoshi

    Number Theory Seminar at Waseda Univ. (Prof. Ki-ichiro Hashimoto and Keiichi Komatsu)  2003.6  Waseda Univ.

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    Venue：Waseda Univ.  

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  • Noether's Problem for D5， F20 and D6 Invited

    Akinari Hoshi

    Number Theory Seminar at Tokyo Metropolitan Univ. (Prof. Yasuhiro Kishi and Toru Komatsu)  2003.5  Tokyo Metropolitan Univ.

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    Venue：Tokyo Metropolitan Univ.  

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  • Quintic Jacobi sums and period polynomials for finite fields

    Akinari Hoshi

    Spring Meeting of the Mathematical Society of Japan  2003.3  The Univ. of Tokyo

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    Venue：The Univ. of Tokyo  

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  • Construction of families of cyclic polynomials with Gaussian period polynomials II

    Ki-ichiro Hashimoto, Akinari Hoshi

    Spring Meeting of the Mathematical Society of Japan  2003.3  The Univ. of Tokyo

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    Venue：The Univ. of Tokyo  

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  • Construction of simple cyclic polynomials of small degree Invited

    Akinari Hoshi

    Workshop: Inverse Galois Problem and Galois Coverings II (Prof. Hirotada Naito and Hiro-o Tokunaga)  2002.12  Kagawa Univ.

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    Venue：Kagawa Univ.  

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  • Multiplicative quadratic forms on algebraic varieties Invited

    Akinari Hoshi

    Number Theory Seminar at Tokyo Metropolitan Univ. (Prof. Kazuo Matsuno)  2002.10  Tokyo Metropolitan Univ.

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    Venue：Tokyo Metropolitan Univ.  

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  • Multiplicative quadratic forms on algebraic varieties Invited

    Akinari Hoshi

    Number Theory Seminar at Waseda Univ. (Prof. Ki-ichiro Hashimoto and Keiichi Komatsu)  2002.10  Waseda Univ.

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    Venue：Waseda Univ.  

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  • Multiplicative quadratic forms on algebraic varieties

    Akinari Hoshi

    Autumn Meeting of the Mathematical Society of Japan  2002.9  Shimane Univ.

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    Venue：Shimane Univ.  

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  • Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations Invited

    Akinari Hoshi

    Workshop: Inverse Galois Problem and Galois Coverings (Prof. Hiro-o Tokunaga)  2002.8  Tokyo Metropolitan Univ.

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    Venue：Tokyo Metropolitan Univ.  

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  • Irreducible polynomials of Gaussian periods and constructions of cyclic polynomials Invited

    Akinari Hoshi

    Number Theory Seminar at Waseda Univ. (Prof. Ki-ichiro Hashimoto and Keiichi Komatsu)  2002.5  Waseda Univ.

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    Venue：Waseda Univ.  

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  • Construction of families of cyclic polynomials with Gaussian period polynomials

    Ki-ichiro Hashimoto, Akinari Hoshi

    Spring Meeting of the Mathematical Society of Japan  2002.3  Meiji Univ.

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    Venue：Meiji Univ.  

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  • Construction of families of cyclic polynomials with Gaussian period polynomials Invited

    Ki-ichiro Hashimoto, Akinari Hoshi

    Workshop on Number Theory at Waseda Univ. (Prof. Ki-ichiro Hashimoto and Keiichi Komatsu)  2002.3  Waseda Univ.

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    Venue：Waseda Univ.  

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Awards

Research Projects

  • Rationality problem for norm one tori in small dimensions

    2021.4 - 2022.3

    System name：Outstanding Paper Award

    Awarding organization：Niigata University

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    Grant type：Competitive

    Grant amount：\100000

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  • Unramified cohomology groups and rationality problem for fields of invariants

    Grant number：19K03418

    2019.4 - 2023.3

    System name：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category：Grant-in-Aid for Scientific Research (C)

    Awarding organization：Japan Society for the Promotion of Science

    HOSHI Akinari

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    Authorship：Principal investigator 

    Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）

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  • Rationality problem for algebraic tori

    2016.4 - 2017.3

    System name：President's Award (Research Grant for Young Researchers)

    Awarding organization：Niigata University

    HOSHI Akinari

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    Authorship：Principal investigator  Grant type：Competitive

    Grant amount：\800000

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  • Rationality problem for fields of invariants

    Grant number：25400027

    2013.4 - 2017.3

    System name：Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category：Grant-in-Aid for Scientific Research (C)

    Awarding organization：Japan Society for the Promotion of Science

    HOSHI Akinari

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    Authorship：Principal investigator 

    Grant amount：\4810000 （ Direct Cost: \3700000 、 Indirect Cost：\1110000 ）

    In view of constructive inverse Galois problem, we studied the rationality problem for fields of invariants under the action of finite groups. The invariant called the unramified Brauer group, which is important for the study of the rationality problem, was completely determined when the order of the group is the fifth power of odd prime p. Even for the unramified cohomology group which is a generalization of the unramified Brauer group, we showed that the non-vanishing of it when the order of the group is the ninth power of odd prime p. We studied Noether's problem and related rationality problems, and got several new results.

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  • A computational research on number fields and coverings with non-commutative Galois groups

    Grant number：22540032

    2010.4 - 2015.3

    System name：Grants-in-Aid for Scientific Research

    Research category：Grant-in-Aid for Scientific Research (C)

    Awarding organization：Japan Society for the Promotion of Science

    TSUNOGAI Hiroshi, TSUZUKI Masao, GOMI Yasushi, UMEGAKI Atsuki, KOMATSU Toru, NAKASUJI Maki, RIKUNA Yuichi, HOSHI Akinari

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    Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）

    Our research intends to study Galois extensions with non-commutative Galois groups concretely. On Cross-Ratio Noether Problem for transitive groups of degree six, we obtained affirmative answers with explicit generators except two non-solvable subgroups. On Relative Rationality between the fixed fields of the fields of cross-ratios and the fields of ratios of differences, for the cases of the symmetric groups, it was shown to be affirmative for odd degrees and to be negative for even degrees. We also obtained negative answers for some subgroups of the symmetric groups of even degrees. We determined the defining equations of the dessins d'enfants of genus one of degree six except one valency list, and confirmed that known Galois invariants of dessins distinguish their Galois orbits in these cases. We showed the existence and non-existence of number fields with given prime inert conditions by means of generic polynomials.

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  • A study on constructive inverse Galois problem

    Grant number：22740028

    2010.4 - 2014.3

    System name：Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

    Research category：Grant-in-Aid for Young Scientists (B)

    Awarding organization：Japan Society for the Promotion of Science

    HOSHI Akinari

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    Authorship：Principal investigator 

    Grant amount：\2340000 （ Direct Cost: \1800000 、 Indirect Cost：\540000 ）

    Galois theory, forms the foundation of modern algebra, founded by Evariste Galois has continued to support the development of state-of-the-art mathematics. In Galois theory, the problem "whether every finite group appears as the Galois group of some field extension or not" is called inverse Galois problem, and is related to the structure of the absolute Galois group of rationals which is an interesting subject in number theory.
    In this research, we gave answers to some problems, e.g. Noether's problem, the field isomorphism problem of generic polynomials, which are related to the inverse Galois problem. By applying this, we also solved some Thue equations.

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  • 単純巡回多項式族に対する同型問題と付随するThue方程式族の整数解への応用

    2009.4 - 2010.3

    System name：学術推進特別重点資金（立教SFR）

    Awarding organization：立教大学

    星 明考

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    Authorship：Principal investigator  Grant type：Competitive

    Grant amount：\500000 （ Direct Cost: \500000 ）

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  • 生成的多項式の共通部分体問題―理論的枠組みの構築と計算代数による応用―

    2008.4 - 2009.3

    System name：学術推進特別重点資金（立教SFR）

    Awarding organization：立教大学

    星 明考

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    Authorship：Principal investigator  Grant type：Competitive

    Grant amount：\500000 （ Direct Cost: \500000 ）

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  • 非可換ガロア拡大の系統的構成および代数多様体上の乗法的二次形式

    2007.4 - 2008.3

    System name：特定課題研究 (2007B-067)

    Awarding organization：早稲田大学

    星 明考

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    Authorship：Principal investigator  Grant type：Competitive

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  • Development of Number Theory based on Generic Polynomials

    Grant number：19540057

    2007 - 2008

    System name：Grants-in-Aid for Scientific Research

    Research category：Grant-in-Aid for Scientific Research (C)

    Awarding organization：Japan Society for the Promotion of Science

    MIYAKE Katsuya, KISHI Yasuhiro, RIKUNA Yuuichi, HOSHI Akinari, KOMATSU Toru

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    Grant amount：\3640000 （ Direct Cost: \2800000 、 Indirect Cost：\840000 ）

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  • ガロア逆問題の構成的研究とその応用について

    2006.4 - 2007.3

    System name：特定課題研究 (2006A-850)

    Awarding organization：早稲田大学

    星 明考

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    Authorship：Principal investigator  Grant type：Competitive

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  • A computational study on extensions of algebraic number fields with non-commutative Galois groups

    Grant number：18540048

    2006 - 2009

    System name：Grants-in-Aid for Scientific Research

    Research category：Grant-in-Aid for Scientific Research (C)

    Awarding organization：Japan Society for the Promotion of Science

    TSUNOGAI Hiroshi, TSUZUKI Masao, UMEGAKI Atsuki, MORIYAMA Tomonori, RIKUNA Yuuichi, HOSHI Akinari, KOMATSU Tooru

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    Grant amount：\4220000 （ Direct Cost: \3500000 、 Indirect Cost：\720000 ）

    Galois Theory is, shortly speaking, a theory of symmetry of numbers. Constructive Galois Theory aims at constructing prescribed symmetry explicitly. In this research, we have treated some cases with non-commutative Galois groups, and constructed explicit polynomials (mainly of degree 5 and 6) with featuring symmetry making use of geometric symmetry. It is significant that the polynomials have brief presentation so that we have obtained some number-theoretic properties.

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  • ガロア逆問題の構成的研究および代数多様体上乗法的な二次形式の理論の展開

    2004.4 - 2006.3

    System name：科学研究費補助金

    星 明考

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    Authorship：Principal investigator  Grant type：Competitive

    Grant amount：\1900000 （ Direct Cost: \1900000 ）

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Teaching Experience

  • 理学基礎演習

    2022
    Institution name：新潟大学

  • 構造数理特別講義

    2022
    Institution name：新潟大学

  • 台湾スプリングセミナー II

    2021
    Institution name：新潟大学

  • 台湾スプリングセミナー I

    2021
    Institution name：新潟大学

  • 専門力アクティブ・ラーニング

    2021
    Institution name：新潟大学

  • 理学スタディ・スキルズ

    2021
    Institution name：新潟大学

  • 先端科学技術総論

    2021
    Institution name：新潟大学

  • 構造数理特別講義

    2020
    -
    2022
    Institution name：新潟大学

  • 代数・幾何学序論B

    2018
    Institution name：新潟大学

  • 線形代数IIA

    2018
    Institution name：新潟大学

  • 代数系IIB

    2017
    Institution name：新潟大学

  • 数学基礎B1

    2017
    Institution name：新潟大学

  • 数学基礎B2

    2017
    Institution name：新潟大学

  • 代数系IIA

    2017
    Institution name：新潟大学

  • 数学演習A

    2017
    -
    2022
    Institution name：新潟大学

  • 数学演習B

    2017
    -
    2022
    Institution name：新潟大学

  • 理学スタディ・スキルズ

    2017
    -
    2021
    Institution name：新潟大学

  • 数学基礎A1

    2017
    Institution name：新潟大学

  • 数学基礎A2

    2017
    Institution name：新潟大学

  • 台湾スプリングセミナー I

    2015
    -
    2018
    Institution name：新潟大学

  • 台湾スプリングセミナー II

    2015
    -
    2018
    Institution name：新潟大学

  • 数理科学文献詳読Ⅱ(数学)

    2015
    Institution name：新潟大学

  • 数理物質科学特定研究Ⅱ(数学)

    2015
    Institution name：新潟大学

  • 数理科学セミナーⅡ(数学)

    2015
    Institution name：新潟大学

  • 代数系II

    2014
    -
    2016
    Institution name：新潟大学

  • 基礎数学B II

    2014
    -
    2016
    Institution name：新潟大学

  • 数理科学セミナーⅠ(数学)

    2014
    -
    2015
    Institution name：新潟大学

  • 数理科学文献詳読Ⅰ(数学)

    2014
    -
    2015
    Institution name：新潟大学

  • 数理物質科学特定研究Ⅰ(数学)

    2014
    -
    2015
    Institution name：新潟大学

  • 数理科学研究発表演習〔中間発表〕(数学)

    2014
    Institution name：新潟大学

  • 自然科学総論Ⅰ

    2014
    Institution name：新潟大学

  • 代数的整数論

    2013
    Institution name：新潟大学

  • 数学講究

    2013
    Institution name：新潟大学

  • 数論

    2013
    Institution name：新潟大学

  • 数学の世界

    2013
    -
    2021
    Institution name：新潟大学

  • 線形代数II

    2013
    -
    2017
    Institution name：新潟大学

  • 数学基礎A

    2013
    -
    2016
    Institution name：新潟大学

  • 数理基礎演習II

    2013
    -
    2016
    Institution name：新潟大学

  • 数学基礎B

    2013
    -
    2016
    Institution name：新潟大学

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Social Activities

  • 整数論と素数と暗号

    Role(s)： Lecturer

    新潟大学  オープンキャンパス模擬授業  2023.8

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    新潟県立新潟高等学校  理数科講演会  2023.6

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    新潟県立新潟江南高等学校  出前講義  2022.11

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    新潟県立新潟高等学校  理数科講演会  2022.6

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    新潟県立長岡向陵高等学校  出前講義  2022.6

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    新潟県立佐渡高等学校  出前講義(Zoom)  2021.8

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    新潟県高等学校教育研究会  講演(Zoom)  2021.7

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  • 整数論と素数と暗号

    Role(s)： Lecturer

    新潟大学  Webオープンキャンパス模擬授業  2020.8

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    新潟県立新潟南高等学校  出前講義  2019.12

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    山梨県立甲府東高等学校  出前講義  2019.10

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  • 整数論と素数と暗号

    Role(s)： Lecturer

    新潟大学  オープンキャンパス模擬授業  2019.8

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    新潟大学  第104回理学部コロキウム  2018.12

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    新潟県立佐渡高等学校  出前講義  2018.8

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  • 整数論と素数と暗号

    Role(s)： Lecturer

    新潟大学  オープンキャンパス模擬授業  2018.8

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  • 整数論と素数と暗号

    Role(s)： Lecturer

    新潟大学  オープンキャンパス模擬授業  2017.8

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  • 整数論と素数と暗号 ―数学は世界を守っている？―

    Role(s)： Lecturer

    新潟大学  第12回市民公開セミナー  2017.3

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  • 素数の世界で方程式を解いてみよう

    Role(s)： Lecturer,　Advisor

    新潟県教育委員会  新潟県高校生理数トップセミナー  2016.11 - 2016.12

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  • 整数論と素数と暗号

    Role(s)： Lecturer

    新潟大学  オープンキャンパス模擬授業  2016.8

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  • 整数論と素数と暗号

    Role(s)： Lecturer

    新潟大学  オープンキャンパス模擬授業  2014.8

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Academic Activities