{
  "id": "1703.10377",
  "version": "v1",
  "published": "2017-03-30T09:31:15.000Z",
  "updated": "2017-03-30T09:31:15.000Z",
  "title": "On a question of Ekedahl and Serre",
  "authors": [
    "Ke Chen",
    "Xin Lu",
    "Kang Zuo"
  ],
  "comment": "and comment is warmly welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we study the Ekedahl-Serre conjecture over number fields. The main result is the existence of an upper bound for the genus of curves whose Jacobians admit isogenies of bounded degrees to self-products of a given elliptic curve over a number field satisfying the Sato-Tate equidistribution, and the technique is motivated by similar results over function field due to Kukulies. A few variants are considered and questions involving more general Shimura subvarieties are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-30T09:31:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G40",
      "14H42"
    ],
    "keywords": [
      "number field",
      "jacobians admit isogenies",
      "general shimura subvarieties",
      "main result",
      "elliptic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}