{
  "id": "0710.4514",
  "version": "v2",
  "published": "2007-10-24T16:52:38.000Z",
  "updated": "2010-06-16T15:29:16.000Z",
  "title": "The External Fundamental Group of an Algebraic Number Field",
  "authors": [
    "T. M. Gendron"
  ],
  "comment": "4 pages",
  "categories": [
    "math.NT",
    "math.AT",
    "math.LO"
  ],
  "abstract": "We associate to every algebraic number field a hyperbolic surface lamination and an external fundamental group: the latter a generalization of the fundamental germ that necessarily contains external (not first order definable) elements. The external fundamental group of the rationals is a split extension of the absolute Galois group, that conjecturally contains a subgroup whose abelianization is isomorphic to the idele class group.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-16T15:29:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R32",
      "14H30",
      "57R30",
      "03C20"
    ],
    "keywords": [
      "external fundamental group",
      "algebraic number field",
      "idele class group",
      "hyperbolic surface lamination",
      "absolute galois group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.4514G"
    }
  }
}