{
  "id": "1601.05939",
  "version": "v1",
  "published": "2016-01-22T10:15:04.000Z",
  "updated": "2016-01-22T10:15:04.000Z",
  "title": "On wild extensions of a p-adic field",
  "authors": [
    "I. Del Corso",
    "R. Dvornicich",
    "M. Monge"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we consider the problem of classifying the isomorphism classes of extensions of degree pk of a p-adic field, restricting to the case of extensions without intermediate fields. We establish a correspondence between the isomorphism classes of these extensions and some Kummer extensions of a suitable field F containing K. We then describe such classes in terms of the representations of Gal(F/K). Finally, for k = 2 and for each possible Galois group G, we count the number of isomorphism classes of the extensions whose normal closure has a Galois group isomorphic to G. As a byproduct, we get the total number of isomorphism classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-22T10:15:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S20",
      "11S15"
    ],
    "keywords": [
      "p-adic field",
      "wild extensions",
      "isomorphism classes",
      "galois group isomorphic",
      "normal closure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}