{
  "id": "0911.5505",
  "version": "v2",
  "published": "2009-11-29T17:52:17.000Z",
  "updated": "2010-03-09T12:12:58.000Z",
  "title": "Points de torsion sur les varietes abeliennes de type GSp",
  "authors": [
    "Marc Hindry",
    "Nicolas Ratazzi"
  ],
  "comment": "31 pages, new section 5, accepted for publication in Journal de l'Institut de Mathematiques de Jussieu",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "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 $\\GSp$ type, i.e. whose Mumford-Tate group is \"generic\" (isomorphic to the group of symplectic similitudes) 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 $A$. The result is unconditional for a product of simple abelian varieties with endomorphism ring $\\Z$ and dimension outside an explicit exceptional set $\\mathcal{S}=\\{4,10,16,32,...\\}$. Furthermore, following a strategy of Serre, we also prove that if the Mumford-Tate conjecture is true for some abelian varieties of $\\GSp$ type, it is then true for a product of such abelian varieties.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-09T12:12:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian variety",
      "varietes abeliennes",
      "type gsp",
      "torsion sur",
      "simple abelian varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.5505H"
    }
  }
}