The group of congruence coefficients of a canonical quadratic form and stable rationality of the \(PSO\) variety
type: Item
instance of: scholarly article
title: The group of congruence coefficients of a canonical quadratic form and stable rationality of the \(PSO\) variety
zbMATH Open document ID: 0855.11019
DOI: 10.1007/BF02112482
published in: Mathematical Notes
publication date: 1995-07-10T00:00:00Z
review text: One of the basic problems in studying the geometric properties of varieties of linear algebraic groups is the problem of rationality. There is Platonov's conjecture of \(K\)-rationality for the variety of a semisimple connected algebraic group \(G\) defined over an arbitrary field \(K\). The following two statements are the main results of the present paper: Theorem 1. Let \(f\) be a canonical quadratic form defined over an arbitrary field \(K\), \(\text{char } K=2\). Then the group \(PSO (f)\) is stably rational over \(K\). Theorem 2. Let \(G\) be an arbitrary compact semisimple \(\mathbb{R}\)-defined algebraic group that does not contain factors of types \(E_i\), \(i=6, 7, 8\). Then the group variety \(G\) is stably rational over \(\mathbb{R}\).
Mathematics Subject Classification ID: 11E57
Mathematics Subject Classification ID: 14L10
Mathematics Subject Classification ID: 11E81
zbMATH DE Number: 771976
zbMATH Keywords: stable rationality
zbMATH Keywords: varieties of linear algebraic groups
zbMATH Keywords: canonical quadratic form
author: V. Chernousov
reviewed by: G. A. Soifer
MaRDI profile type: Publication
cites work: Q4692288
cites work: Q3946274
cites work: Q3340974
cites work: Q5675788
full work available at URL: https://doi.org/10.1007/bf02112482
OpenAlex ID: W2019922475
description: scientific article; zbMATH DE number 771976