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

DOI:
https://doi.org/10.1090/S0002-9939-97-03637-X

MathSciNet review:
1353401

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the Jacobian of the Fermat curve of exponent 5 and let . We compute the groups , , , where is the unique quadratic subfield of . As an application, we present a new proof that there are no -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:
https://doi.org/10.1090/S0002-9939-97-03637-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