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
Full text: dvi.gz 32 k, dvi 72 k, ps.gz 679 k, pdf.gz 184 k, pdf 206 k.