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arXiv:math/0208118 [math.NT]AbstractReferencesReviewsResources

Kummer theory of abelian varieties and reductions of Mordell-Weil groups

Tom Weston

Published 2002-08-14Version 1

Let A be an abelian variety over a number field F with End(A/F) commutative. Let S be a subgroup of A(F) and let x be a point of A(F). Suppose that for almost all places v of F the reduction of x modulo v lies in the reduction of S modulo v. In this paper we prove that x must then lie in S + A(F)_tors. This provides a partial answer to a generalization (due to W. Gajda) of the support problem of Erdos.

Categories: math.NT, math.AC
Subjects: 11G10, 14K15, 13F05
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