{
  "id": "math/9802092",
  "version": "v1",
  "published": "1998-02-19T14:38:15.000Z",
  "updated": "1998-02-19T14:38:15.000Z",
  "title": "On just infinite pro-p-groups and arithmetically profinite extensions of local fields",
  "authors": [
    "Ivan Fesenko"
  ],
  "comment": "15 pages, AMSTeX",
  "categories": [
    "math.GR",
    "math.NT"
  ],
  "abstract": "The wild group is the group of wild automorphisms of a local field of characteristic p. In this paper we apply Fontaine-Wintenberger's theory of fields of norms to study the structure of the wild group. In particular we provide a new short proof of R. Camina's theorem which says that every pro-p-group with countably many open sugroups is isomorphic to a closed subgroup of the wild group. We study some closed subgroups T of the wild group whose commutator subgroup is unusually small. Realizing the group T as the Galois group of arithmetically profinite extensions of p-adic fields we answer affirmatively Coates--Greenberg's problem on deeply ramified extensions of local fields. Finally using the subgroup T we show that the wild group is not analytic over commutative complete local noetherian integral domains with finite residue field of characteristic p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-02-19T14:38:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S15",
      "20F99",
      "22E99"
    ],
    "keywords": [
      "arithmetically profinite extensions",
      "local field",
      "wild group",
      "infinite pro-p-groups",
      "complete local noetherian integral domains"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......2092F"
    }
  }
}