{
  "id": "1307.2441",
  "version": "v1",
  "published": "2013-07-09T13:14:46.000Z",
  "updated": "2013-07-09T13:14:46.000Z",
  "title": "On Selmer groups of abelian varieties over $\\ell$-adic Lie extensions of global function fields",
  "authors": [
    "Andrea Bandini",
    "Maria Valentino"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $F$ be a global function field of characteristic $p>0$ and $A/F$ an abelian variety. Let $K/F$ be an $\\l$-adic Lie extension ($\\l\\neq p$) unramified outside a finite set of primes $S$ and such that $\\Gal(K/F)$ has no elements of order $\\l$. We shall prove that, under certain conditions, $Sel_A(K)_\\l^\\vee$ has no nontrivial pseudo-null submodule.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-09T13:14:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11G35"
    ],
    "keywords": [
      "global function field",
      "adic lie extension",
      "abelian variety",
      "selmer groups",
      "nontrivial pseudo-null submodule"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.2441B"
    }
  }
}