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arXiv · 1603.07718

Totaro's Question for Tori of Low Rank

Reed Leon Gordon-Sarney
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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 $d \geq 1$, then does $X$ have a closed \'etale 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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Reed Leon Gordon-Sarney. 2016-03-24. Totaro's Question for Tori of Low Rank. https://arxiv.org/abs/1603.07718

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