On birational equivalence of algebraic tori
type: Item
instance of: scholarly article
title: On birational equivalence of algebraic tori
zbMATH Open document ID: 1222.14109
published in: Journal of Mathematical Sciences (New York)
publication date: 2010-01-19T00:00:00Z
review text: The author studies the birational classification of algebraic tori over non-closed fields. Given a field \(k\), let \({\overline k}\) be the algebraic closure of \(k\). A \(k\)-torus is an algebraic group \(T\) such that \(T\otimes_k{\overline k}\) is isomorphic to a connected diagonal group over \({\overline k}\). Two \(k\) varieties \(X_1\) and \(X_2\) are said to be stably equivalent if there exist \(p,m\in{\mathbb N}\) such that \(X_1\times {\mathbb A}^p\) is birationally isomorphic to \(X_2\times {\mathbb A}^m\). A variety is stably rational if it is stably equivalent to affine space. The author proves the conjecture that if a torus is rationally stable, then it is rational.
reviewed by: Lucy Moser-Jauslin
Mathematics Subject Classification ID: 14M20
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 14E08
zbMATH DE Number: 5660109
zbMATH Keywords: rational variety
zbMATH Keywords: algebraic tori
zbMATH Keywords: stable equivalence
author: V. E. Voskresenskiĭ
MaRDI profile type: Publication
full work available at URL: s10958-009-9543-7
OpenAlex ID: W2093684849
cites work: Stably rational non rational varieties
cites work: Q5607044
cites work: Stably rational algebraic tori
DOI: 10.1007/S10958-009-9543-7
description: scientific article; zbMATH DE number 5660109