{
  "id": "2012.12666",
  "version": "v1",
  "published": "2020-12-23T14:00:46.000Z",
  "updated": "2020-12-23T14:00:46.000Z",
  "title": "On local criteria for the unit equation and the asymptotic Fermat's Last Theorem",
  "authors": [
    "Nuno Freitas",
    "Alain Kraus",
    "Samir Siksek"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let F be a totally real number field of odd degree. We prove several purely local criteria for the asymptotic Fermat's Last Theorem to hold over F, and also for the non-existence of solutions to the unit equation over F. For example, if 2 totally ramifies and 3 splits completely in F, then the asymptotic Fermat's Last Theorem holds over F.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-23T14:00:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D41"
    ],
    "keywords": [
      "asymptotic fermats",
      "unit equation",
      "totally real number field",
      "theorem holds",
      "purely local criteria"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}