Totaro's question for simply connected groups of low rank
type: Item
instance of: scholarly article
title: Totaro's question for simply connected groups of low rank
zbMATH Open document ID: 1302.11015
author: Jodi Black
author: R. Parimala
published in: Pacific Journal of Mathematics
publication date: 2014-12-30T00:00:00Z
review text: Let \(k\) be a field and let \(G\) be a connected linear algebraic group over \(k\). In [Duke Math. J. 121, No. 3, 425--455 (2004; Zbl 1048.11031)], \textit{B. Totaro} asked whether a torsor \(X\) under \(G\) and over \(k\) which admits a zero cycle of degree \(d\), also admits a closed étale point of degree dividing \(d.\) (This generalizes a question of Serre concerning the case \(d=1.\)) The authors obtain an affirmative answer when \(G\) is a simply connected, semisimple group of rank at most 2 and \(2k \neq 0\).
Mathematics Subject Classification ID: 11E72
Mathematics Subject Classification ID: 11E57
Mathematics Subject Classification ID: 11E81
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 6382642
zbMATH Keywords: zero cycles
zbMATH Keywords: Galois cohomology
zbMATH Keywords: classical groups
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
full work available at URL: pjm.2014.269.257
OpenAlex ID: W2058272318
DOI: 10.2140/PJM.2014.269.257
description: scientific article; zbMATH DE number 6382642