{
  "id": "1009.4026",
  "version": "v5",
  "published": "2010-09-21T09:25:59.000Z",
  "updated": "2012-03-21T00:23:27.000Z",
  "title": "Brauer-Manin pairing, class field theory and motivic homology",
  "authors": [
    "Takao Yamazaki"
  ],
  "comment": "25 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "For a smooth proper variety over a $p$-adic field, the Brauer group and abelian fundamental group are related to the higher Chow groups by the Brauer-Manin pairing and the class field theory. We generalize this relation to smooth (possibly non-proper) varieties, using the motivic homology and the tame version of Wiesend's ideal class group. Several examples are discussed.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-03-21T00:23:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S25",
      "14G20",
      "14C25"
    ],
    "keywords": [
      "class field theory",
      "motivic homology",
      "brauer-manin pairing",
      "wiesends ideal class group",
      "smooth proper variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4026Y"
    }
  }
}