{
  "id": "0803.3346",
  "version": "v3",
  "published": "2008-03-23T21:15:54.000Z",
  "updated": "2009-04-17T15:04:30.000Z",
  "title": "Counting points of homogeneous varieties over finite fields",
  "authors": [
    "Michel Brion",
    "Emmanuel Peyre"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be an algebraic variety over a finite field $\\bF_q$, homogeneous under a linear algebraic group. We show that the number of rational points of $X$ over $\\bF_{q^n}$ is a periodic polynomial function of $q^n$ with integer coefficients. Moreover, the shifted periodic polynomial function, where $q^n$ is formally replaced with $q^n + 1$, is shown to have non-negative coefficients.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-04-17T15:04:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A50",
      "14G15",
      "14L30",
      "14M17"
    ],
    "keywords": [
      "finite field",
      "homogeneous varieties",
      "counting points",
      "linear algebraic group",
      "shifted periodic polynomial function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.3346B"
    }
  }
}