{
  "id": "1504.03367",
  "version": "v1",
  "published": "2015-04-09T16:15:40.000Z",
  "updated": "2015-04-09T16:15:40.000Z",
  "title": "Approximation on abelian varieties by its subgroups",
  "authors": [
    "Arash Rastegar"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "In this paper, we introduce an algebro-geometric formulation for Faltings' theorem on diophantine approximation on abelian varieties using an improvement of Faltings-Wustholz observation over number ?fields. In fact, we prove that, for any geometrically irreducible sub-variety E of an abelian variety A and any ?finitely generated subgroup F of A(C) we have an estimate of the form d_v(E;x) >cH(x)^d for for some constant c where d_v(E;x) denotes the distance of a point x in F outside E and v is a place of K. This was proved before, only for F being the set of rational points of A over a number ?field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-09T16:15:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian variety",
      "rational points",
      "algebro-geometric formulation",
      "diophantine approximation",
      "faltings-wustholz observation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150403367R"
    }
  }
}