Specializations of finitely generated subgroups of abelian varieties

Masser, D. W.

doi:10.1090/S0002-9947-1989-0974783-6

Specializations of finitely generated subgroups of abelian varieties
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Trans. Amer. Math. Soc. 311 (1989), 413-424 Request permission

Abstract:

Given a generic Mordell-Weil group over a function field, we can specialize it down to a number field. It has been known for some time that the resulting homomorphism of groups is injective "infinitely often". We prove that this is in fact true "almost always", in a sense that is quantitatively nearly best possible.

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