Specializations of Finitely Generated Subgroups of Abelian Varieties

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1989Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 311, page 413 (issn: 0002-9947,

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Authors: Masser, D. W.;

doi: 10.2307/2001034 , 10.1090/s0002-9947-1989-0974783-6

Specializations of Finitely Generated Subgroups of Abelian Varieties

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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.

Keywords

abelian varieties, Mordell-Weil group, Rational points, Abelian varieties and schemes, degree, Algebraic theory of abelian varieties, height

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