{
  "id": "math/0405318",
  "version": "v7",
  "published": "2004-05-17T09:33:17.000Z",
  "updated": "2007-02-16T18:51:57.000Z",
  "title": "Deligne's integrality theorem in unequal characteristic and rational points over finite fields; and Appendix (w/Pierre Deligne)",
  "authors": [
    "Hélène Esnault"
  ],
  "comment": "16 pages",
  "journal": "Ann. of Math. (2) 164 (2006), no. 2, 715--730",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "If $V$ is a smooth projective variety defined over a local field $K$ with finite residue field, so that its \\'etale cohomology over the algebraic closure $\\bar{K}$ is supported in codimension 1, then the mod $p$ reduction of a projective regular model carries a rational point. As a consequence, if the Chow group of 0-cycles of $V$ over a large algebraically closed field is trivial, then the mod $p$ reduction of a projective regular model carries a rational point.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2007-02-16T18:51:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational point",
      "delignes integrality theorem",
      "unequal characteristic",
      "w/pierre deligne",
      "finite fields"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5318E"
    }
  }
}