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

Tom Weston
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Abstract

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.

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Tom Weston. 2002-08-14. Kummer theory of abelian varieties and reductions of Mordell-Weil groups. https://doi.org/10.4064/aa110-1-6

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