{
  "id": "math/0203220",
  "version": "v2",
  "published": "2002-03-21T14:13:49.000Z",
  "updated": "2002-12-02T17:59:27.000Z",
  "title": "Rationally connected varieties over finite fields",
  "authors": [
    "János Kollár",
    "Endre Szabó"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a geometrically rational (or more generally, separably rationally connected) variety over a finite field K. We prove that if K is large enough then X contains many rational curves defined over K. As a consequence we prove that R-equivalence is trivial on X if K is large enough. These imply that if Y is defined over a local field and it has good, separably rationally connected reduction then the Chow group of zero cycles is trivial for any residue field. R-equivalence is also trivial if the residue field is large enough.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-12-02T17:59:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G15",
      "14J20",
      "14M20",
      "14C15",
      "14G20"
    ],
    "keywords": [
      "rationally connected varieties",
      "finite field",
      "residue field",
      "local field",
      "rational curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3220K"
    }
  }
}