Totaro's Question for Tori of Low Rank
Reed Leon Gordon-Sarney

TL;DR
This paper affirms Totaro's question for algebraic tori of rank at most 2, establishing a link between zero-cycles and étale points in this context.
Contribution
It provides the first positive answer to Totaro's question specifically for low-rank algebraic tori, filling a gap in the literature.
Findings
Confirmed Totaro's question for tori of rank ≤ 2
Established existence of étale points dividing the degree of zero-cycles
Extended understanding of torsor properties in algebraic geometry
Abstract
Let be a smooth connected linear algebraic group and be a -torsor. Totaro asked: if admits a zero-cycle of degree , then does have a closed \'etale point of degree dividing ? This question is entirely unexplored in the literature for algebraic tori. We settle Totaro's question affirmatively for algebraic tori of rank .
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