Totaro’s question for tori of low rank

Gordon-Sarney, Reed

doi:10.1090/tran/7052

Totaro’s question for tori of low rank
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by Reed Leon Gordon-Sarney PDF

Trans. Amer. Math. Soc. 370 (2018), 3245-3264

Abstract:

Let $G$ be a smooth connected linear algebraic group and let $X$ be a $G$-torsor. Totaro asked: if $X$ admits a zero-cycle of degree $d \geq 1$, then does $X$ have a closed étale point of degree dividing $d$? This question is entirely unexplored in the literature for algebraic tori. We settle Totaro’s question affirmatively for algebraic tori of rank $\leq 2$.

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