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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Mordell-Weil groups of the Jacobian of the 5-th Fermat curve
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by Pavlos Tzermias PDF
Proc. Amer. Math. Soc. 125 (1997), 663-668 Request permission

Abstract:

Let $J_{5}$ denote the Jacobian of the Fermat curve of exponent 5 and let $K=Q(\zeta _{5})$. We compute the groups $J_{5}(K)$, $J_{5}(K^{+})$, $J_{5}(Q)$, where $K^{+}$ is the unique quadratic subfield of $K$. As an application, we present a new proof that there are no $K$-rational points on the 5-th Fermat curve, except the so called “points at infinity".
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Additional Information
  • Pavlos Tzermias
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • Email: tzermias@math.berkeley.edu, tzermias@crm.es
  • Received by editor(s): November 5, 1994
  • Received by editor(s) in revised form: September 1, 1995
  • Communicated by: William W. Adams
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 663-668
  • MSC (1991): Primary 14H25, 14G05; Secondary 11D41
  • DOI: https://doi.org/10.1090/S0002-9939-97-03637-X
  • MathSciNet review: 1353401