{
  "id": "1409.7544",
  "version": "v1",
  "published": "2014-09-26T11:43:28.000Z",
  "updated": "2014-09-26T11:43:28.000Z",
  "title": "An upper bound on the number of rational points of arbitrary projective varieties over finite fields",
  "authors": [
    "Alain Couvreur"
  ],
  "categories": [
    "math.AG",
    "math.CO",
    "math.NT"
  ],
  "abstract": "We give an upper bound on the number of rational points of an arbitrary Zariski closed subset of a projective space over a finite field. This bound depends only on the dimensions and degrees of the irreducible components and holds for very general varieties, even reducible and non equidimensional. As a consequence, we prove a conjecture of Ghorpade and Lachaud on the maximal number of rational points of an equidimensional projective variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-26T11:43:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J20",
      "11C25"
    ],
    "keywords": [
      "rational points",
      "arbitrary projective varieties",
      "upper bound",
      "finite field",
      "arbitrary zariski closed subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.7544C"
    }
  }
}