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Torsion in Mordell-Weil groups of Fermat Jacobians

Published online by Cambridge University Press:  04 December 2007

PAVLOS TZERMIAS
PAVLOS TZERMIAS
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720
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Abstract

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We study the torsion in the Mordell-Weil group of the Jacobian of the Fermat curve of exponent $p$ over the cyclotomic field obtained by adjoining a primitive $p$-th root of 1 to $Q$. We show that for all (except possibly one) proper subfields of this cyclotomic field, the torsion parts of the corresponding Mordell-Weil groups are elementary abelian $p$-groups.

Keywords

TorsionMordell-Weil groupsFermat Jacobians
Type
Research Article
Information
Compositio Mathematica , Volume 106 , Issue 1 , March 1997 , pp. 1 - 9
Copyright
© 1997 Kluwer Academic Publishers