On the problem of detecting linear dependence for products of abelian varieties and tori
| dc.creator | Perucca, Antonella | |
| dc.date | 2008-11-10 | |
| dc.date.accessioned | 2026-07-07T10:17:14Z | |
| dc.date.available | 2026-07-07T10:17:14Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0811.1495 | |
| dc.identifier | http://arxiv.org/abs/0811.1495 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173783 | |
| dc.subject | Number Theory | |
| dc.subject | 14K15 (Primary) 14G25, 14L10 (Secondary) | |
| dc.title | On the problem of detecting linear dependence for products of abelian varieties and tori | |
| dc.type | text |