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- W2949277640 abstract "Let G be the product of an abelian variety and a torus defined over a number field K. Let R be a point in G(K) and let L be a finitely generated subgroup of G(K). Suppose that for all but finitely many primes p of K the point (R mod p) belongs to (L mod p). Does it follow that R belongs to L? We answer this question affirmatively in three cases: if L is cyclic; if L is a free left End_K G-submodule of G(K); if L has a set of generators (as a group) which is a basis of a free left End_K G-submodule of G(K). In general we prove that there exists an integer m (depending only on G, K and the rank of L) such that mR belongs to the left End_K G-submodule of G(K) generated by L." @default.
- W2949277640 created "2019-06-27" @default.
- W2949277640 creator A5022080623 @default.
- W2949277640 date "2008-11-10" @default.
- W2949277640 modified "2023-10-03" @default.
- W2949277640 title "On the problem of detecting linear dependence for products of abelian varieties and tori" @default.
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