{
  "id": "0707.1143",
  "version": "v3",
  "published": "2007-07-08T15:31:51.000Z",
  "updated": "2009-01-28T07:29:58.000Z",
  "title": "Selmer groups for elliptic curves in Z_l^d-extensions of function fields of characteristic p",
  "authors": [
    "Andrea Bandini",
    "Ignazio Longhi"
  ],
  "comment": "Final version to appear in Annales de l'Institut Fourier",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $F$ be a function field of characteristic $p>0$, $\\F/F$ a Galois extension with $Gal(\\F/F)\\simeq \\Z_l^d$ (for some prime $l\\neq p$) and $E/F$ a non-isotrivial elliptic curve. We study the behaviour of Selmer groups $Sel_E(L)_r$ ($r$ any prime) as $L$ varies through the subextensions of $\\F$ via appropriate versions of Mazur's Control Theorem. As a consequence we prove that $Sel_E(\\F)_r$ is a cofinitely generated (in some cases cotorsion) $\\Z_r[[Gal(\\F/F)]]$-module.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-01-28T07:29:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H52",
      "11R23"
    ],
    "keywords": [
      "function field",
      "selmer groups",
      "characteristic",
      "non-isotrivial elliptic curve",
      "mazurs control theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.1143B"
    }
  }
}