{
  "id": "1105.2427",
  "version": "v2",
  "published": "2011-05-12T11:17:09.000Z",
  "updated": "2011-12-15T20:08:05.000Z",
  "title": "Small Galois groups that encode valuations",
  "authors": [
    "Ido Efrat",
    "Jan Minac"
  ],
  "comment": "Final version. To appear in Acta Arithmetica",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime number and let $F$ be a field containing a root of unity of order $p$. We prove that a certain very small canonical Galois group $(G_F)_{[3]}$ over $F$ encodes the valuations on $F$ whose value group is not $p$-divisible and which satisfy a variant of Hensel's lemma.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-15T20:08:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12J10"
    ],
    "keywords": [
      "small galois groups",
      "encode valuations",
      "small canonical galois group",
      "prime number",
      "value group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.2427E"
    }
  }
}