Skip Garibaldi and Detlev W. Hoffmann: Totaro's Question for G_2, F_4, and E_6,

Submission: 2004, Dec 7

In a 2004 paper, Totaro asked whether a G-torsor X which 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.

2000 Mathematics Subject Classification: 11E72, 20G15

Keywords and Phrases: algebraic group, exceptional group, torsor, Albert algebra, Rost invariant, Pfister form, linkage, Galois cohomology, flat cohomology

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