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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mordell-Weil groups of the Jacobian
of the 5-th Fermat curve


Author: Pavlos Tzermias
Journal: Proc. Amer. Math. Soc. 125 (1997), 663-668
MSC (1991): Primary 14H25, 14G05; Secondary 11D41
MathSciNet review: 1353401
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03637-X
PII: S 0002-9939(97)03637-X
Received by editor(s): November 5, 1994
Received by editor(s) in revised form: September 1, 1995
Communicated by: William W. Adams
Article copyright: © Copyright 1997 American Mathematical Society