{
  "id": "0804.1658",
  "version": "v1",
  "published": "2008-04-10T10:19:14.000Z",
  "updated": "2008-04-10T10:19:14.000Z",
  "title": "On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields",
  "authors": [
    "S. Vigni"
  ],
  "comment": "20 pages, to appear in J. Number Theory",
  "doi": "10.1016/j.jnt.2007.11.007",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional eigenspace relative to a fixed complex ring class character provided that the projection onto this eigenspace of a suitable Drinfeld-Heegner point is nonzero. This represents the analogue in the function field setting of a theorem for rational elliptic curves due to Bertolini and Darmon, and at the same time is a generalization of the main result proved by Brown in his monograph on Heegner modules. As in the number field case, our proof employs Kolyvagin-type arguments, and the cohomological machinery is started up by the control on the Galois structure of the torsion of E provided by classical results of Igusa in positive characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-10T10:19:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "14G10"
    ],
    "keywords": [
      "global function field",
      "ring class eigenspaces",
      "mordell-weil groups",
      "proof employs kolyvagin-type arguments",
      "fixed complex ring class character"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.1658V"
    }
  }
}