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Totaro's question for tori of low rank


Author: Reed Leon Gordon-Sarney
Journal: Trans. Amer. Math. Soc. 370 (2018), 3245-3264
MSC (2010): Primary 11E72; Secondary 20G15, 14G05
DOI: https://doi.org/10.1090/tran/7052
Published electronically: November 17, 2017
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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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Additional Information

Reed Leon Gordon-Sarney
Affiliation: Department of Mathematics & Computer Science, Emory University, Atlanta, Georgia 30322

DOI: https://doi.org/10.1090/tran/7052
Received by editor(s): April 12, 2016
Received by editor(s) in revised form: July 25, 2016
Published electronically: November 17, 2017
Article copyright: © Copyright 2017 by the author

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