{
  "id": "math/0612147",
  "version": "v1",
  "published": "2006-12-06T09:46:05.000Z",
  "updated": "2006-12-06T09:46:05.000Z",
  "title": "Counting points on varieties over finite fields of small characteristic",
  "authors": [
    "Alan G. B. Lauder",
    "Daqing Wan"
  ],
  "comment": "To appear in: \"Algorithmic number theory: lattices, number fields, curves and cryptography\", J.P. Buhler and P. Stevenhagen (ed.), Math. Sci. Res. Inst. Publ. 44. (Submitted July 2001; Accepted October 2002.)",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We present a deterministic polynomial time algorithm for computing the zeta function of an arbitrary variety of fixed dimension over a finite field of small characteristic. One consequence of this result is an efficient method for computing the order of the group of rational points on the Jacobian of a smooth geometrically connected projective curve over a finite field of small characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-06T09:46:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y16",
      "11T99",
      "14Q15"
    ],
    "keywords": [
      "finite field",
      "small characteristic",
      "counting points",
      "deterministic polynomial time algorithm",
      "smooth geometrically connected projective curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12147L"
    }
  }
}