Totaro's question for simply connected groups of low rank

Jodi Black and Raman Parimala

Vol. 269 (2014), No. 2, 257–267

DOI: 10.2140/pjm.2014.269.257

Abstract

Let $k$ be a field and let $G$ be a connected linear algebraic group over $k$. In a 2004 paper, 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 $d$. We consider this question in the setting where $G$ is a simply connected, semisimple group of rank at most 2 and $k$ is of characteristic different from 2.

Keywords

zero cycles, Galois cohomology, classical groups

Mathematical Subject Classification 2010

Primary: 11E72

Secondary: 11E57, 11E81

Milestones

Received: 28 November 2012

Revised: 19 February 2013

Accepted: 25 February 2013

Published: 26 July 2014