Totaro's Question on Zero-Cycles on Torsors

Abstract

Let $G$ be a smooth connected linear algebraic group and $X$ be a $G$-torsor. Totaro asked: if $X$ admits a zero-cycle of degree $d\ge 1$, then does $X$ have a closed étale point of degree dividing $d$? While the literature contains affirmative answers in some special cases, we give an example to show that the answer is negative in general.

8 pages

References in corpus (1)

• Totaro's question for G_2, F_4, and E_6

Cited by in corpus (1)

• Closed points on cubic hypersurfaces