{
  "id": "1505.05620",
  "version": "v1",
  "published": "2015-05-21T07:07:28.000Z",
  "updated": "2015-05-21T07:07:28.000Z",
  "title": "Torsion pour les varietes abeliennes de type I et II",
  "authors": [
    "Marc Hindry",
    "Nicolas Ratazzi"
  ],
  "comment": "33 pages, in french",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let A be an abelian variety defined over a number field K, the number of torsion points rational over a finite extension L is bounded polynomially in terms of the degree [L : K]. When A is isogenous to a product of simple abelian varieties of type I or II in Albert classification and is \"fully of Lefschetz type\", i.e. whose Mumford-Tate group is the group of symplectic similitudes commuting with endomorphisms and which satisfy the Mumford-Tate conjecture, we compute the optimal exponent for this bound in terms of the dimensions of the abelian subvarieties of A and their rings of endomorphisms. The result is unconditional for a product of simple abelian varieties of type I or II with odd relative dimension. Extending work of Serre, Pink and Hall, we also prove that the Mumford-Tate conjecture is true for a few new cases for such abelian varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-21T07:07:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian variety",
      "torsion pour",
      "varietes abeliennes",
      "simple abelian varieties",
      "mumford-tate conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "fr",
      "license": "arXiv",
      "status": "editable"
    }
  }
}