{
  "id": "1204.5441",
  "version": "v3",
  "published": "2012-04-24T17:33:25.000Z",
  "updated": "2012-10-16T10:41:44.000Z",
  "title": "Abelian varieties over number fields, tame ramification and big Galois image",
  "authors": [
    "Sara Arias-de-Reyna",
    "Christian Kappen"
  ],
  "comment": "16 pages; revised according to the referee's remarks and suggestions regarding the overall structure of the paper",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given a natural number n and a number field K, we show the existence of an integer \\ell_0 such that for any prime number \\ell\\geq \\ell_0, there exists a finite extension F/K, unramified in all places above \\ell, together with a principally polarized abelian variety A of dimension n over F such that the resulting \\ell-torsion representation \\rho_{A,\\ell} from G_F to GSp(A[\\ell](\\bar{F})) is surjective and everywhere tamely ramified. In particular, we realize GSp_{2n}(\\mathbb{F}_\\ell) as the Galois group of a finite tame extension of number fields F'/F such that F is unramified above \\ell.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-10-16T10:41:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11G10",
      "11K40"
    ],
    "keywords": [
      "number field",
      "big galois image",
      "abelian variety",
      "tame ramification",
      "finite tame extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.5441A"
    }
  }
}