{
  "id": "1412.6888",
  "version": "v1",
  "published": "2014-12-22T07:04:09.000Z",
  "updated": "2014-12-22T07:04:09.000Z",
  "title": "Class field theory for open curves over local fields",
  "authors": [
    "Toshiro Hiranouchi"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the class field theory for an open curve over a local field. In particular, we determine the kernel and the cokernel of the reciprocity homomorphism and obtain the one to one correspondence between the set of finite abelian \\'etale coverings which are not completely split and the set of finite index open subgroups of the id\\`ele class group as in the classical class field theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-22T07:04:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local field",
      "open curve",
      "finite index open subgroups",
      "finite abelian etale coverings",
      "classical class field theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.6888H"
    }
  }
}