{
  "id": "math/0405164",
  "version": "v2",
  "published": "2004-05-10T05:10:04.000Z",
  "updated": "2005-03-23T22:38:54.000Z",
  "title": "Arithmetic cohomology over finite fields and special values of zeta-functions",
  "authors": [
    "Thomas H. Geisser"
  ],
  "comment": "28 pages, revised version",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We construct a cohomology theory with compact support H^i_c(X_ar,Z(n))$ for separated schemes of finite type over a finite field, which should play a role analog to Lichtenbaum's Weil-etale cohomology groups for smooth and projective schemes. In particular, if Tate's conjecture holds and rational and numerical equivalence agree up to torsion, then the groups H^i_c(X_ar,Z(n)) are finitely generated, form an integral version of l-adic cohomology with compact support, and admit a formula for the special values of the zeta-function of X.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-03-23T22:38:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "special values",
      "finite field",
      "arithmetic cohomology",
      "zeta-function",
      "lichtenbaums weil-etale cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5164G"
    }
  }
}