A. Yamasaki

activity

20092026

most citedRationality problem for algebraic tori

19 citations · 30 across the 22 of their papers we have counts for

collaborators

24 papers

math.AG2026

Rationality problem for norm one tori of tensor products of étale algebras and Hasse norm principle

Mathieu Florence, Akinari Hoshi, Aiichi Yamasaki

Let $k$ be a field. Let $A = \prod_{i = 1}^{r} K_{i}$ and $B = \prod_{j = 1}^{s} E_{j}$ be étale $k$ -algebras where $K_{i}$ and $E_{j}$ are finite separable field extensions of $k$ with $[K_{i} : k] = m_{i}$ …

math.NT2025

Hasse norm principle for Heisenberg extensions of degree $p^{3}$

Akinari Hoshi, Aiichi Yamasaki

Let $k$ be a global field and $p$ be an odd prime number. We give a necessary and sufficient condition for the Hasse norm principle for separable field extensions $K / k$ , i.e. the d…

math.NT2025

Hasse norm principle for metacyclic extensions with trivial Schur multiplier

Akinari Hoshi, Aiichi Yamasaki

Let $k$ be a global field, $K / k$ be a finite separable field extension and $L / k$ be the Galois closure of $K / k$ with Galois groups $G = Gal (L / k)$ and $H = Gal (L / K) ⪇ G$ .…

math.NT2024

Norm one tori and Hasse norm principle, III: Degree $16$ case

Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

Let $k$ be a field, $T$ be an algebraic $k$ -torus, $X$ be a smooth $k$ -compactification of $T$ and $Pic X$ be the Picard group of $\overline{X}=X\times_k\overline…

math.AG2023

Rationality problem for norm one tori for small non-Galois extensions: Symmetric, alternating and linear group cases including stably rational $PSL_{2} (F_{2^{d}})$ cases with $d = 1, 2, 3$

Akinari Hoshi, Aiichi Yamasaki

Let $k$ be a field, $K / k$ be a separable field extension of degree $n$ and $L / k$ be the Galois closure of $K / k$ . Let $G = Gal (L / k)$ and $H = Gal (L / K) ⪇ G$ with $[G : H] = n$ …

math.AG2023

Rationality problem for norm one tori for dihedral extensions

Akinari Hoshi, Aiichi Yamasaki

We give a complete answer to the rationality problem (up to stable $k$ -equivalence) for norm one tori $R_{K / k}^{(1)} (G_{m})$ of $K / k$ whose Galois closures $L / k$ are dihedra…

math.NT2022

Hasse norm principle for $M_{11}$ and $J_{1}$ extensions

Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

We give a necessary and sufficient condition for the Hasse norm principle for field extensions $K / k$ when the Galois groups $Gal (L / k)$ of the Galois closure $L / k$ of $K / k$ ar…

math.AG2021★ 1 cited

Birational classification for algebraic tori

Akinari Hoshi, Aiichi Yamasaki

We give a stably birational classification for algebraic tori of dimensions $3$ and $4$ over a field $k$ . First, we define the weak stably equivalence of algebraic tori and show th…

math.AG2020★ 1 cited

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

Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

Let $k$ be a field, $T$ be an algebraic $k$ -torus, $X$ be a smooth $k$ -compactification of $T$ and $Pic X$ be the Picard group of $\overline{X}=X\times_k\overline…

math.AG2019★ 3 cited

Norm one tori and Hasse norm principle

Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki

Let $k$ be a field and $T$ be an algebraic $k$ -torus. In 1969, over a global field $k$ , Voskresenskii proved that there exists an exact sequence $0\to A(T)\to H^1(k,{\rm Pic}\,\ove…

math.AG2019

An application of cohomological invariants

Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

Let $G$ be a finite group, $k$ be a field and $G \to G L (V_{reg})$ be the regular representation of $G$ over $k$ . Then $G$ acts naturally on the rational function field $k(V_{\rm…

math.AG2018

Rationality problem for norm one tori in small dimensions

Sumito Hasegawa, Akinari Hoshi, Aiichi Yamasaki

We classify stably/retract rational norm one tori in dimension $n - 1$ for $n = 2^{e}$ $(e \geq 1)$ is a power of $2$ and $n = 12, 14, 15$ . Retract non-rationality of norm one tori for prim…

math.AG2018★ 1 cited

Rationality problem for norm one tori

Akinari Hoshi, Aiichi Yamasaki

We classify stably/retract rational norm one tori in dimension $p - 1$ where $p$ is a prime number and in dimension up to ten with some minor exceptions.

math.AG2018

A two-dimensional rationality problem and intersections of two quadrics

Akinari Hoshi, Ming-chang Kang, Hidetaka Kitayama +1

Let $k$ be a field with char $k \neq = 2$ and $k$ be not algebraically closed. Let $a \in k ∖ k^{2}$ and $L = k (a) (x, y)$ be a field extension of $k$ where $x, y$ are algebraic…

math.AG2017★ 1 cited

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

Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

Let $k$ be a field and $G$ be a finite group acting on the rational function field $k (x_{g} : g \in G)$ by $k$ -automorphisms defined as $h (x_{g}) = x_{h g}$ for any $g, h \in G$ . We denote t…

math.AG2016★ 1 cited

Multiplicative Invariant Fields of Dimension \le 6

Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

The finite subgroups of $G L_{4} (Z)$ are classified up to conjugation in \cite{BBNWZ}; in particular, there exist $710$ non-conjugate finite groups in $G L_{4} (Z)$ . Each finite…

math.AG2015

Degree Three Unramified Cohomology Groups

Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

Let $p$ be an odd prime number. Peyre shows that there is a group $G$ of order $p^{12}$ such that $H_{n r}^{3} (C (G), Q / Z)$ is non-trivial. Using Peyre's method, we are…

math.NT2015★ 1 cited

Rationality problems for relation modules of dihedral groups

Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

Let D_n be the dihedral group of order 2n where n \ge 2, 1 \to R \to F \to D_n \to 1 be a free presentation of D_n. R^{ab}:=R/[R,R] becomes a \bm{Z}[D_n]-lattice. We will study the…

math.AG2014★ 2 cited

Rationality problem of conic bundles

Aiichi Yamasaki

Let $k$ be a field with char $k \neq = 2$ , $X$ be an affine surface defined by the equation $z^{2} = P (x) y^{2} + Q (x)$ where $P (x), Q (x) \in k [x]$ are separable polynomials. We will investi…

math.NT2014

Class Numbers and Algebraic Tori

Akinari Hoshi, Ming-chang Kang, Aiichi Yamasaki

Let $p$ be an odd prime number, $D_{p}$ be the dihedral group of order $2 p$ , $h_{p}$ and $h_{p}^{+}$ be the class numbers of $Q (ζ_{p})$ and $Q (ζ_{p} + ζ_{p}^{- 1})$ respectively. Theorem…

math.AG2013

Rationality problem of generalized Châtelet surfaces

Aiichi Yamasaki

The surface $z^{2} = a y^{2} + P (x), a \in k, P (x) \in k [x]$ is not $k$ -rational, if $a \neq \in k^{2}$ and $P (x)$ satisfies some conditions. This result essentially due to Iskovskih but…

math.AG2012★ 19 cited

Rationality problem for algebraic tori

Akinari Hoshi, Aiichi Yamasaki

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…

math.AG2009

Rationality problem of three-dimensional monomial group actions

Akinari Hoshi, Hidetaka Kitayama, Aiichi Yamasaki

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 of acting on $K (x, y, z)$ by…

math.NT2009

Negative solutions to three-dimensional monomial Noether problem

Aiichi Yamasaki

Three-dimensional monomial Noether problem can have negative solutions for 8 groups by the suitable choice of the coefficients. We find the necessary and sufficient condition for t…

Rationality problem for norm one tori of tensor products of étale algebras and Hasse norm principle

Hasse norm principle for Heisenberg extensions of degree p3

Hasse norm principle for metacyclic extensions with trivial Schur multiplier

Norm one tori and Hasse norm principle, III: Degree 16 case

Rationality problem for norm one tori for small non-Galois extensions: Symmetric, alternating and linear group cases including stably rational PSL2​(F2d​) cases with d=1,2,3

Rationality problem for norm one tori for dihedral extensions

Hasse norm principle for M11​ and J1​ extensions

Birational classification for algebraic tori

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

Norm one tori and Hasse norm principle

An application of cohomological invariants

Rationality problem for norm one tori in small dimensions

Rationality problem for norm one tori

A two-dimensional rationality problem and intersections of two quadrics

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

Multiplicative Invariant Fields of Dimension \le 6

Degree Three Unramified Cohomology Groups

Rationality problems for relation modules of dihedral groups

Rationality problem of conic bundles

Class Numbers and Algebraic Tori

Rationality problem of generalized Châtelet surfaces

Rationality problem for algebraic tori

Rationality problem of three-dimensional monomial group actions

Negative solutions to three-dimensional monomial Noether problem

Hasse norm principle for Heisenberg extensions of degree $p^{3}$

Norm one tori and Hasse norm principle, III: Degree $16$ case

Rationality problem for norm one tori for small non-Galois extensions: Symmetric, alternating and linear group cases including stably rational $PSL_{2} (F_{2^{d}})$ cases with $d = 1, 2, 3$

Hasse norm principle for $M_{11}$ and $J_{1}$ extensions

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

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