On the problem of detecting linear dependence for products of abelian varieties and tori

dc.creatorPerucca, Antonella
dc.date2008-11-10
dc.date.accessioned2026-07-07T10:17:14Z
dc.date.available2026-07-07T10:17:14Z
dc.descriptionLet 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.
dc.identifierhttps://arxiv.org/abs/0811.1495
dc.identifierhttp://arxiv.org/abs/0811.1495
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173783
dc.subjectNumber Theory
dc.subject14K15 (Primary) 14G25, 14L10 (Secondary)
dc.titleOn the problem of detecting linear dependence for products of abelian varieties and tori
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