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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 $\leq 2$.
References
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Additional Information
  • Reed Leon Gordon-Sarney
  • Affiliation: Department of Mathematics & Computer Science, Emory University, Atlanta, Georgia 30322
  • Received by editor(s): April 12, 2016
  • Received by editor(s) in revised form: July 25, 2016
  • Published electronically: November 17, 2017
  • © Copyright 2017 by the author
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 3245-3264
  • MSC (2010): Primary 11E72; Secondary 20G15, 14G05
  • DOI: https://doi.org/10.1090/tran/7052
  • MathSciNet review: 3766848