A. Yamasaki

activity

20092026

most citedRationality problem for algebraic tori

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

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17 papers · 1 filter

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.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.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.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.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…

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

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

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 problem of conic bundles

Rationality problem of generalized Châtelet surfaces

Rationality problem for algebraic tori

Rationality problem of three-dimensional monomial group actions

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 $d = 1, 2, 3$

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

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