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Journal of the London Mathematical Society 2006 73(2):325-338; doi:10.1112/S0024610705022489
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© The London Mathematical Society

Totaro's Question on Zero-Cycles on G2, F4 and E6 Torsors

Skip Garibaldi and Detlev W. Hoffmann

Department of Mathematics and Computer Science, Emory University Atlanta, GA 30322, USA skip{at}member.ams.org
Division of Pure Mathematics, School of Mathematical Sciences, University of Nottingham University Park, Nottingham NG7 2RD, United Kingdom Detlev.Hoffmann{at}Nottingham.ac.uk

Received 23 December 2004.

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 G2, type F4, or simply connected of type E6. We extend the list of cases where the answer is ‘yes’ to all groups of type G2 and some nonsplit groups of type F4 and E6. No assumption on the characteristic of the base field is made. The key tool is a lemma regarding linkage of Pfister forms.


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