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TOTARO'S QUESTION ON ZERO-CYCLES ON $G_2$, $F_4$ AND $E_6$ TORSORS

Published online by Cambridge University Press:  24 April 2006

SKIP GARIBALDI
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USAskip@member.ams.org
DETLEV W. HOFFMANN
Affiliation:
Division of Pure Mathematics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United KingdomDetlev.Hoffmann@Nottingham.ac.uk
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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 étale 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.

Type
Notes and Papers
Copyright
The London Mathematical Society 2006

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TOTARO'S QUESTION ON ZERO-CYCLES ON $G_2$, $F_4$ AND $E_6$ TORSORS
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