{
  "id": "math/0601438",
  "version": "v3",
  "published": "2006-01-18T13:51:12.000Z",
  "updated": "2007-01-29T15:02:10.000Z",
  "title": "Point counting in families of hyperelliptic curves",
  "authors": [
    "H. Hubrechts"
  ],
  "comment": "33 pages. Changes: major revision",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let E_G be a family of hyperelliptic curves defined by Y^2=Q(X,G), where Q is defined over a small finite field of odd characteristic. Then with g in an extension degree n field over this small field, we present a deterministic algorithm for computing the zeta function of the curve E_g by using Dwork deformation in rigid cohomology. The time complexity of the algorithm is O(n^(2.667)) and it needs O(n^(2.5)) bits of memory. A slight adaptation requires only O(n^2) space, but costs time O(n^3). An implementation of this last result turns out to be quite efficient for n big enough.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-01-29T15:02:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14Q05",
      "11G20",
      "12H25",
      "14F30",
      "14G50"
    ],
    "keywords": [
      "hyperelliptic curves",
      "point counting",
      "small finite field",
      "quite efficient",
      "odd characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1438H"
    }
  }
}