{
  "id": "math/0402230",
  "version": "v5",
  "published": "2004-02-13T16:01:47.000Z",
  "updated": "2004-07-07T11:33:53.000Z",
  "title": "Congruences for rational points on varieties over finite fields",
  "authors": [
    "N. Fakhruddin",
    "C. S. Rajan"
  ],
  "comment": "Minor changes",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We show that the number of rational points on the fibres of a proper morphism of smooth varieties over a finite field k whose generic fibre has a ``trival'' Chow group of zero cycles is congruent to 1 mod |k|. As a consequence we prove that there is a rational point on any degeneration of a smooth proper rationally chain connected variety over a finite field. We also obtain a generalisation of the Chevalley-Warning theorem.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2004-07-07T11:33:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational point",
      "finite field",
      "congruences",
      "proper rationally chain connected variety",
      "smooth proper rationally chain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2230F"
    }
  }
}