Totaro's question for G_2, F_4, and E_6
Algebraic Geometry
2009-05-23 v1
Abstract
In a 2004 paper, Totaro asked whether a G-torsor X that has a zero-cycle of degree d > 0 will necessarily have a closed etale point of degree dividing d, where G is a connected algebraic group. This question is closely related to several conjectures regarding exceptional algebraic groups. Totaro gave a positive answer to his question in the following cases: G simple, split, and of type G_2, type F_4, or simply connected of type E_6. We extend the list of cases where the answer is "yes" to all groups of type G_2 and some nonsplit groups of type F_4 and E_6. No assumption on the characteristic of the base field is made. The key tool is a lemma regarding linkage of Pfister forms.
Cite
@article{arxiv.math/0412148,
title = {Totaro's question for G_2, F_4, and E_6},
author = {Skip Garibaldi and Detlev Hoffmann},
journal= {arXiv preprint arXiv:math/0412148},
year = {2009}
}
Comments
15 pages