{
  "id": "2210.01396",
  "version": "v1",
  "published": "2022-10-04T06:09:10.000Z",
  "updated": "2022-10-04T06:09:10.000Z",
  "title": "Class field theory, Hasse principles and Picard-Brauer duality for two-dimensional local rings",
  "authors": [
    "Takashi Suzuki"
  ],
  "comment": "48 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We draw concrete consequences from our arithmetic duality for two-dimensional local rings with perfect residue field. These consequences include class field theory, Hasse principles for coverings and $K_{2}$ and a duality between divisor class groups and Brauer groups. To obtain these, we analyze the structures of the ind-pro-algebraic groups obtained earlier and prove some finiteness properties about them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-04T06:09:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G45",
      "14F20",
      "19F05",
      "11S25"
    ],
    "keywords": [
      "class field theory",
      "two-dimensional local rings",
      "hasse principles",
      "picard-brauer duality",
      "draw concrete consequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}