{
  "id": "0811.1495",
  "version": "v1",
  "published": "2008-11-10T16:04:47.000Z",
  "updated": "2008-11-10T16:04:47.000Z",
  "title": "On the problem of detecting linear dependence for products of abelian varieties and tori",
  "authors": [
    "Antonella Perucca"
  ],
  "categories": [
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-10T16:04:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K15",
      "14G25",
      "14L10"
    ],
    "keywords": [
      "detecting linear dependence",
      "abelian variety",
      "free left",
      "g-submodule",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.1495P"
    }
  }
}