記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

researchmap

その他リンク： https://www.ams.org/mcom/2022-91-337/S0025-5718-2022-03735-2/S0025-5718-2022-03735-2.pdf

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

DOI： 10.1007/s00229-021-01313-7

researchmap

その他リンク： https://link.springer.com/article/10.1007/s00229-021-01313-7/fulltext.html

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

DOI： 10.1007/s11856-021-2117-1

researchmap

その他リンク： https://link.springer.com/article/10.1007/s11856-021-2117-1/fulltext.html

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Project Euclid  

DOI： 10.3792/pjaa.97.001

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）  

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Duke University Press  

DOI： 10.1215/21562261-2019-0008

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：American Mathematical Society ({AMS})  

DOI： 10.1090/mcom/3469

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Elsevier {BV}  

DOI： 10.1016/j.jalgebra.2019.08.008

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Elsevier {BV}  

DOI： 10.1016/j.jalgebra.2019.04.015

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）  

researchmap

記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：Springer Berlin Heidelberg  

DOI： 10.1007/978-3-662-43799-5_7

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

掲載種別：研究論文（学術雑誌）   出版者・発行元：Adam Mickiewicz University (Euclid)  

DOI： 10.7169/facm/2012.47.1.3

Scopus

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：東北大学  

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

CiNii Article

CiNii Books

researchmap

その他リンク： https://jlc.jst.go.jp/DN/JALC/00348817179?from=CiNii

記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）  

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：立教大学  

DOI： 10.14992/00008648

CiNii Article

CiNii Books

researchmap

記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：Hindustan Book Agency  

DOI： 10.1007/978-93-86279-46-0

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：JAPAN ACAD  

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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：AMER MATHEMATICAL SOC  

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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：AMER MATHEMATICAL SOC  

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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：JAPAN ACAD  

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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：JAPAN ACAD  

DOI： 10.3792/pjaa.82.87

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：AMER MATHEMATICAL SOC  

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

Web of Science

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

Scopus

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Japan Academy  

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

Scopus

researchmap

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：JAPAN ACAD  

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

Web of Science

researchmap

開催地：新潟大学 + Zoom   国名：日本国  

researchmap

開催地：Zoom (Meijo)  

researchmap

開催地：Zoom (Chiba)   国名：日本国  

researchmap

開催地：Zoom (Oberwolfach)  

researchmap

開催地：Zoom (Kobe)  

researchmap

開催地：Zoom (Tokushima)   国名：日本国  

researchmap

開催地：日本大学   国名：日本国  

researchmap

開催地：日本大学   国名：日本国  

researchmap

開催地：静岡大学   国名：日本国  

researchmap

開催地：倉敷シーサイドホテル   国名：日本国  

researchmap

開催地：新潟大学   国名：日本国  

researchmap

開催地：高知大学   国名：日本国  

researchmap

開催地：新潟大学   国名：日本国  

researchmap

開催地：東北公益文科大学公益ホール  

researchmap

開催地：東北公益文科大学公益ホール  

researchmap

開催地：国立台湾大学   国名：台湾  

researchmap

開催地：山形大学   国名：日本国  

researchmap

開催地：新潟大学   国名：日本国  

researchmap

開催地：東京工業大学   国名：日本国  

researchmap

開催地：東京工業大学   国名：日本国  

researchmap

開催地：東京工業大学   国名：日本国  

researchmap

開催地：Universite Pierre-et-Marie-Curie (Paris VI)   国名：フランス共和国  

researchmap

開催地：国立台湾大学   国名：台湾  

researchmap

開催地：新潟大学  

researchmap

開催地：東京大学  

researchmap

開催地：東京大学  

researchmap

開催地：新潟大学  

researchmap

開催地：城崎国際アートセンター  

researchmap

開催地：国立台湾大学  

researchmap

開催地：東京理科大学  

researchmap

開催地：九州大学  

researchmap

開催地：山形大学  

researchmap

開催地：ボルドー大学  

researchmap

開催地：大阪大学  

researchmap

開催地：首都大学東京  

researchmap

開催地：首都大学東京  

researchmap

開催地：首都大学東京  

researchmap

開催地：関西学院大学  

researchmap

開催地：新潟大学  

researchmap

開催地：京都大学  

researchmap

開催地：京都大学  

researchmap

開催地：国立台湾大学  

researchmap

開催地：島根大学  

researchmap

開催地：島根大学  

researchmap

開催地：京都大学  

researchmap

開催地：愛知工業大学本山キャンパス  

researchmap

開催地：山形大学  

researchmap

開催地：新潟大学駅南キャンパスときめいと  

researchmap

開催地：東京理科大学  

researchmap

開催地：筑波大学  

researchmap

開催地：筑波大学  

researchmap

開催地：筑波大学  

researchmap

開催地：筑波大学  

researchmap

開催地：名古屋大学  

researchmap

開催地：首都大学東京秋葉原サテライトキャンパス  

researchmap

開催地：京都大学  

researchmap

開催地：国立彰化師範大学  

researchmap

開催地：デブレツェン大学  

researchmap

開催地：山形大学  

researchmap

開催地：明治大学  

researchmap

開催地：新潟大学  

researchmap

開催地：高知大学  

researchmap

開催地：国立台湾大学  

researchmap

開催地：Coex  

researchmap

開催地：山形大学  

researchmap

開催地：学習院大学  

researchmap

開催地：山形大学  

researchmap

開催地：早稲田大学  

researchmap

開催地：国立台湾大学  

researchmap

開催地：名古屋大学  

researchmap

開催地：京都大学  

researchmap

開催地：立教大学  

researchmap

開催地：京都大学数理解析研究所  

researchmap

開催地：早稲田大学  

researchmap

開催地：九州大学  

researchmap

開催地：九州大学  

researchmap

開催地：山形大学  

researchmap

開催地：国立台湾大学  

researchmap

開催地：九州大学  

researchmap

開催地：高知大学  

researchmap

開催地：東北大学  

researchmap

開催地：山形大学  

researchmap

開催地：日本大学  

researchmap

開催地：東京理科大学  

researchmap

開催地：東京理科大学  

researchmap

開催地：埼玉大学  

researchmap

開催地：関西学院大学  

researchmap

開催地：立教大学  

researchmap

開催地：国立台湾大学  

researchmap

開催地：国立台湾大学  

researchmap

開催地：国立台湾大学  

researchmap

開催地：名古屋大学  

researchmap

開催地：名古屋大学  

researchmap

開催地：慶應義塾大学  

researchmap

開催地：関西学院大学  

researchmap

開催地：金沢大学サテライト・プラザ  

researchmap

開催地：金沢大学サテライト・プラザ  

researchmap

開催地：JALリゾート シーホークホテル福岡  

researchmap

開催地：大阪大学  

researchmap

開催地：大阪大学  

researchmap

開催地：日本大学  

researchmap

開催地：東北大学  

researchmap

開催地：東京工業大学  

researchmap

開催地：徳島大学  

researchmap

開催地：近畿大学  

researchmap

開催地：山形大学  

researchmap

開催地：香港城市大学  

researchmap

開催地：京都大学数理解析研究所  

researchmap

開催地：首都大学東京  

researchmap

開催地：山形大学  

researchmap

開催地：早稲田大学  

researchmap

開催地：国立台湾大学  

researchmap

開催地：山形大学  

researchmap

開催地：神奈川大学  

researchmap

開催地：国立清華大学  

researchmap

開催地：ハリスチャンドラ研究所  

researchmap

開催地：大阪市立大学  

researchmap

開催地：九州大学  

researchmap

開催地：山形大学  

researchmap

開催地：早稲田大学  

researchmap

開催地：鹿児島大学  

researchmap

開催地：ミュンヘン工科大学  

researchmap

開催地：ハイデルベルク大学  

researchmap

開催地：ザーラント大学  

researchmap

開催地：レーゲンスブルク大学  

researchmap

開催地：レーゲンスブルク大学  

researchmap

開催地：レーゲンスブルク大学  

researchmap

開催地：レーゲンスブルク大学  

researchmap

開催地：東京都立大学  

researchmap

開催地：筑波大学  

researchmap

開催地：早稲田大学  

researchmap

開催地：香川大学  

researchmap

開催地：千葉大学  

researchmap

開催地：早稲田大学  

researchmap

開催地：東京都立大学  

researchmap

開催地：東京大学  

researchmap

開催地：東京大学  

researchmap

開催地：香川大学  

researchmap

開催地：東京都立大学  

researchmap

開催地：早稲田大学  

researchmap

開催地：島根大学  

researchmap

開催地：東京都立大学  

researchmap

開催地：早稲田大学  

researchmap

開催地：明治大学  

researchmap

開催地：早稲田大学  

researchmap

researchmap

researchmap

researchmap

researchmap

researchmap

researchmap

researchmap

researchmap

researchmap

researchmap

researchmap

researchmap

researchmap

researchmap