{
  "id": "1201.2310",
  "version": "v2",
  "published": "2012-01-11T14:40:36.000Z",
  "updated": "2012-04-02T00:50:49.000Z",
  "title": "Constructing non-trivial elements of the Shafarevich-Tate group of an Abelian Variety over a Number Field",
  "authors": [
    "Amod Agashe",
    "Saikat Biswas"
  ],
  "comment": "18 pages",
  "doi": "10.1016/j.jnt.2012.10.014",
  "categories": [
    "math.NT"
  ],
  "abstract": "The second part of the Birch and Swinnerton-Dyer (BSD) conjecture gives a conjectural formula for the order of the Shafarevich-Tate group of an elliptic curve in terms of other computable invariants of the curve. Cremona and Mazur initiated a theory that can often be used to verify the BSD conjecture by constructing non-trivial elements of the Shafarevich-Tate group of an elliptic curve by means of the Mordell-Weil group of an ambient curve. In this paper, we generalize Cremona and Mazur's work and give precise conditions under which such a construction can be made for the Shafarevich-Tate group of an abelian variety over a number field. We then give an extension of our general result that provides new theoretical evidence for the BSD conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-02T00:50:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G40"
    ],
    "keywords": [
      "shafarevich-tate group",
      "constructing non-trivial elements",
      "abelian variety",
      "number field",
      "bsd conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.2310A"
    }
  }
}