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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 generic abelian varieties in the unitary case


Author: Alice Silverberg
Journal: Proc. Amer. Math. Soc. 104 (1988), 723-728
MSC: Primary 14K10; Secondary 11G10, 11G15, 14D05, 14K22
MathSciNet review: 929425
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Abstract: The generic fibre of a fibre system of polarized abelian varieties with level structure, and with endomorphism structure coming from a CM-field, is defined over the function field of the moduli space for the abelian varieties. We prove that the points on this generic abelian variety which are defined over the function field of the moduli space form a finite group. The methods of proof generalize those of Mordell- Weil groups of generic abelian varieties, Invent. Math. 81 (1985), 71-106, to which this paper is a sequel.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0929425-7
PII: S 0002-9939(1988)0929425-7
Article copyright: © Copyright 1988 American Mathematical Society