{
  "id": "2302.00222",
  "version": "v1",
  "published": "2023-02-01T03:56:30.000Z",
  "updated": "2023-02-01T03:56:30.000Z",
  "title": "A converse to the Hasse-Arf theorem",
  "authors": [
    "G. Griffith Elder",
    "Kevin Keating"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $L/K$ be a finite Galois extension of local fields. The Hasse-Arf theorem says that if Gal$(L/K)$ is abelian then the upper ramification breaks of $L/K$ must be integers. We prove the following converse to the Hasse-Arf theorem: Let $G$ be a nonabelian group which is isomorphic to the Galois group of some totally ramified extension $E/F$ of local fields with residue characteristic $p>2$. Then there is a totally ramified extension of local fields $L/K$ with residue characteristic $p$ such that Gal$(L/K)\\cong G$ and $L/K$ has at least one nonintegral upper ramification break.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-01T03:56:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S15"
    ],
    "keywords": [
      "local fields",
      "nonintegral upper ramification break",
      "residue characteristic",
      "totally ramified extension",
      "hasse-arf theorem says"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}