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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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Explicit descent for Jacobians of prime power cyclic covers of the projective line
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by Edward F. Schaefer PDF
Trans. Amer. Math. Soc. 370 (2018), 3487-3505 Request permission

Abstract:

The Jacobian of a cyclic cover of the projective line is isogenous to a product of abelian subvarieties, one for each positive divisor of the degree of the cover. In this article, we show how to compute a Selmer group that bounds the Mordell-Weil rank for each abelian subvariety corresponding to a non-trivial prime power divisor of the degree. In the case that the Chabauty condition holds for that abelian subvariety, we show how to bound the number of rational points on the curve.
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Additional Information
  • Edward F. Schaefer
  • Affiliation: Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, California 95053
  • Email: eschaefer@scu.edu
  • Received by editor(s): July 29, 2015
  • Received by editor(s) in revised form: August 10, 2016
  • Published electronically: December 1, 2017
  • Additional Notes: The author is grateful for the hospitality of the Mathematisches Institut at the Universität Bayreuth, where much of this research was done, and to his host there, Michael Stoll, for many useful conversations. This article benefited from useful comments from the referees.
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 3487-3505
  • MSC (2010): Primary 11G30; Secondary 11G10, 14G25, 14H40, 14H45
  • DOI: https://doi.org/10.1090/tran/7060
  • MathSciNet review: 3766856