{
  "id": "1206.2767",
  "version": "v2",
  "published": "2012-06-13T11:02:48.000Z",
  "updated": "2013-04-04T14:21:44.000Z",
  "title": "Control Theorems for l-adic Lie extensions of global function fields",
  "authors": [
    "Andrea Bandini",
    "Maria Valentino"
  ],
  "comment": "21 pages, revised arguments in sections 2 and 4",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let F be a global function field of characteristic p>0, K/F an l-adic Lie extension unramified outside a finite set of places S and A/F an abelian variety without complex multiplication. We study Sel_A(K)_l^\\vee (the Pontrjagin dual of the Selmer group) and (under some mild hypotheses) prove that it is a finitely generated Z_l[[\\Gal(K/F)]]-module via generalizations of Mazur's Control Theorem. If Gal(K/F) has no elements of order l and contains a closed normal subgroup H such that Gal(K/F)/H\\simeq Z_l, we are able to give sufficient conditions for Sel_A(K)_l^\\vee to be finitely generated as Z_l[[H]]-module and, consequently, a torsion Z_l[[\\Gal(K/F)]]-module. We deal with both cases l\\neq p and l=p.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-04T14:21:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global function field",
      "l-adic lie extension unramified outside",
      "mazurs control theorem",
      "finite set",
      "abelian variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.2767B"
    }
  }
}