{
  "id": "1011.0357",
  "version": "v3",
  "published": "2010-11-01T15:50:09.000Z",
  "updated": "2011-10-15T17:46:24.000Z",
  "title": "Determination of the number of isomorphism classes of extensions of a $\\kp$-adic field",
  "authors": [
    "Maurizio Monge"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT",
    "math.CO",
    "math.GR"
  ],
  "abstract": "We deduce a formula enumerating the isomorphism classes of extensions of a $\\kp$-adic field $K$ with given ramification $e$ and inertia $f$. The formula follows from a simple group-theoretic lemma, plus the Krasner formula and an elementary class field theory computation. It shows that the number of classes only depends on the ramification and inertia of the extensions $K/\\Q_p$, and $K(\\zeta_{p^m})/K$ obtained adding the $p^m$-th roots of 1, for all $p^m$ dividing $e$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-15T17:46:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S15",
      "12B25",
      "05A19",
      "20D60"
    ],
    "keywords": [
      "adic field",
      "isomorphism classes",
      "extensions",
      "elementary class field theory computation",
      "determination"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.0357M"
    }
  }
}