{
  "id": "1108.4975",
  "version": "v1",
  "published": "2011-08-25T00:51:30.000Z",
  "updated": "2011-08-25T00:51:30.000Z",
  "title": "A bound on the number of points of a curve in projective space over a finite field",
  "authors": [
    "Masaaki Homma"
  ],
  "comment": "9 pages, presented at the Fq10 conference",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a nondegenerate irreducible curve $C$ of degree $d$ in ${\\Bbb P}^r$ over ${\\Bbb F}_q$ with $r \\geq 3$, we prove that the number $N_q(C)$ of ${\\Bbb F}_q$-points of $C$ satisfies the inequality $N_q(C) \\leq (d-1)q +1$, which is known as Sziklai's bound if $r=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-25T00:51:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G15",
      "11G20",
      "14H25"
    ],
    "keywords": [
      "finite field",
      "projective space",
      "sziklais bound",
      "nondegenerate irreducible curve"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4975H"
    }
  }
}