Torsors on the affine line
type: Item
instance of: scholarly article
title: Torsors on the affine line
zbMATH Open document ID: 1062.14061
author: Yanyan Li
published in: Transformation Groups
publication date: 2002-01-01T00:00:00Z
review text: Let \(G\) be a connected algebraic reductive group over an arbitrary field \(k\). The classification of \(G\)-torsors over the projective line was given by \textit{A. Grothendieck} [Am. J. Math. 79, 121--138 (1957; Zbl 0079.17001)] for the case when \(k\) is an algebraically closed field of characteristic zero and by \textit{G. Harder} [Invent. Math. 6, 107--149 (1968; Zbl 0186.25902)] for a general field. Torsors over an affine line for a general field have been studied by \textit{M. S. Raghunathan} and \textit{A. Ramanathan} [Proc. Indian Acad. Sci., Math. Sci. 93, 137--145 (1984; Zbl 0587.14007)]. In this article, the author gives a new proof of a result of Raghunathan and Ramanathan stating that any \(G\)-torsor on the affine line which is trivial over the separable closure of \(k\) comes from a \(G\)-torsor over \(\text{Spec}\,k\).
reviewed by: Lucy Moser-Jauslin
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 1885650
zbMATH Keywords: torsors
zbMATH Keywords: principal homogeneous space
zbMATH Keywords: separable closure of a field
MaRDI profile type: Publication
full work available at URL: s00031-002-0012-3
OpenAlex ID: W2048002029
DOI: 10.1007/S00031-002-0012-3
description: scientific article; zbMATH DE number 1885650