{
  "id": "1604.04563",
  "version": "v1",
  "published": "2016-04-15T16:43:55.000Z",
  "updated": "2016-04-15T16:43:55.000Z",
  "title": "Torsion points and height jumping in higher-dimensional families of abelian varieties",
  "authors": [
    "David Holmes"
  ],
  "comment": "28 pages. Includes some material previously contained in arXiv:1412.8207",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "In 1983 Silverman and Tate showed that the set of points in a 1-dimensional family of abelian varieties where a section of infinite order has `small height' is finite. We conjecture a generalisation to higher-dimensional families, where we replace `finite' by `not Zariski dense'. We show that this conjecture would imply the Uniform Boundedness Conjecture for torsion points on abelian varieties. We then prove a few special cases of this new conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-15T16:43:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "14G40"
    ],
    "keywords": [
      "abelian varieties",
      "higher-dimensional families",
      "torsion points",
      "height jumping",
      "uniform boundedness conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404563H"
    }
  }
}