{
  "id": "math/0204330",
  "version": "v1",
  "published": "2002-04-29T15:43:43.000Z",
  "updated": "2002-04-29T15:43:43.000Z",
  "title": "Relative K-theory and class field theory for arithmetic surfaces",
  "authors": [
    "Alexander Schmidt"
  ],
  "comment": "32 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "In this paper we extend the unramified class field theory for arithmetic surfaces of K. Kato and S. Saito to the relative case. Let X be a regular proper arithmetic surface and let Y be the support of divisor on X. Let CH_0(X,Y) denote the relative Chow group of zero cycles and let \\tilde \\pi_1^t(X,Y)^ {ab} denote the abelianized modified tame fundamental group of (X,Y) (which classifies finite etale abelian covings of X-Y which are tamely ramified along Y and in which every real point splits completely). THEOREM: There exists a natural reciprocity isomorphism rec: CH_0(X,Y) --> \\tilde \\pi_1^t(X,Y)^{ab}. Both groups are finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-04-29T15:43:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19F05",
      "11R37"
    ],
    "keywords": [
      "class field theory",
      "relative k-theory",
      "modified tame fundamental group",
      "classifies finite etale abelian covings",
      "natural reciprocity isomorphism rec"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......4330S"
    }
  }
}