{
  "id": "math/0303143",
  "version": "v2",
  "published": "2003-03-12T15:39:37.000Z",
  "updated": "2003-05-12T15:51:49.000Z",
  "title": "The p-part of Tate-Shafarevich groups of elliptic curves can be arbitrarily large",
  "authors": [
    "Remke Kloosterman"
  ],
  "comment": "Second version; The final section has been changed to correct a mistake in the first version. Some reference are added",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper it is shown that for every prime p>5 the dimension of the p-torsion in the Tate-Shafarevich group of E/K can be arbitrarily large, where E is an elliptic curve defined over a number field K, with [K:Q] bounded by a constant depending only on p. From this we deduce that the dimension of the p-torsion in the Tate-Shafarevich group of A/Q can be arbitrarily large, where A is an abelian variety, with dim A bounded by a constant depending only on p.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-05-12T15:51:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G18"
    ],
    "keywords": [
      "tate-shafarevich group",
      "arbitrarily large",
      "number field",
      "constant depending",
      "abelian variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......3143K"
    }
  }
}