{
  "id": "0902.2533",
  "version": "v3",
  "published": "2009-02-15T09:29:09.000Z",
  "updated": "2013-10-08T00:38:36.000Z",
  "title": "Albanese varieties with modulus over a perfect field",
  "authors": [
    "Henrik Russell"
  ],
  "comment": "revised version, technical parts slightly more general",
  "journal": "Algebra & Number Theory Vol. 7, No. 4 (2013), 853-892",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let X be a smooth proper variety over a perfect field k of arbitrary characteristic. Let D be an effective divisor on X with multiplicity. We introduce an Albanese variety Alb(X, D) of X of modulus D as a higher dimensional analogon of the generalized Jacobian of Rosenlicht-Serre with modulus for smooth proper curves. Basing on duality of 1-motives with unipotent part (which are introduced here), we obtain explicit and functorial descriptions of these generalized Albanese varieties and their dual functors. We define a relative Chow group of zero cycles w.r.t. the modulus D and show that Alb(X, D) is a universal quotient of this Chow group. As an application we can rephrase Lang's class field theory of function fields of varieties over finite fields in explicit terms.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-08T00:38:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L10",
      "14C15",
      "11G45"
    ],
    "keywords": [
      "perfect field",
      "rephrase langs class field theory",
      "chow group",
      "smooth proper curves",
      "albanese variety alb"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2533R"
    }
  }
}