{
  "id": "1402.5193",
  "version": "v2",
  "published": "2014-02-21T03:00:32.000Z",
  "updated": "2015-01-08T19:57:20.000Z",
  "title": "Indices of inseparability in towers of field extensions",
  "authors": [
    "Kevin Keating"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be a local field whose residue field has characteristic $p$ and let $L/K$ be a finite separable totally ramified extension of degree $n=ap^{\\nu}$. The indices of inseparability $i_0,i_1,...,i_{\\nu}$ of $L/K$ were defined by Fried in the case char$(K)=p$ and by Heiermann in the case char$(K)=0$; they give a refinement of the usual ramification data for $L/K$. The indices of inseparability can be used to construct \"generalized Hasse-Herbrand functions\" $\\phi_{L/K}^j$ for $0\\le j\\le\\nu$. In this paper we give an interpretation of the values $\\phi_{L/K}^j(c)$ for natural numbers $c$. We use this interpretation to study the behavior of generalized Hasse-Herbrand functions in towers of field extensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-21T03:00:32.000Z",
      "abstract": "Let K be a local field whose residue field has characteristic p and let L/K be a finite separable totally ramified extension of degree n=ap^{\\nu}. The indices of inseparability i_0,i_1,...,i_{\\nu} of L/K were defined by Fried in the case char(K)=p and by Heiermann in the case char(K)=0; they give a refinement of the usual ramification data for L/K. The indices of inseparability can be used to construct \"generalized Hasse-Herbrand functions\" \\phi_{L/K}^j for 0\\le j\\le\\nu. In this paper we give an interpretation of the values \\phi_{L/K}^j(c) for natural numbers c. We use this interpretation to study the behavior of generalized Hasse-Herbrand functions in towers of field extensions.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-08T19:57:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S15"
    ],
    "keywords": [
      "field extensions",
      "inseparability",
      "generalized hasse-herbrand functions",
      "usual ramification data",
      "finite separable totally ramified extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.5193K"
    }
  }
}