{
  "id": "math/0201311",
  "version": "v1",
  "published": "2002-01-31T06:13:50.000Z",
  "updated": "2002-01-31T06:13:50.000Z",
  "title": "On the nonexistence of certain curves of genus two",
  "authors": [
    "Everett W. Howe"
  ],
  "comment": "LaTeX, 13 pages",
  "journal": "Compos. Math. 140 (2004) 581--592",
  "doi": "10.1112/S0010437X03000757",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove that if q is a power of an odd prime then there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (2-2q)x^2 + q^2. Our proof uses the Brauer relations in a biquadratic extension of Q to show that every principally polarized abelian surface over F_q with the given characteristic polynomial splits over F_{q^2} as a product of polarized elliptic curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-01-31T06:13:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "11G10",
      "11R65",
      "14G15",
      "14H25"
    ],
    "keywords": [
      "nonexistence",
      "characteristic polynomial splits",
      "polarized elliptic curves",
      "frobenius equal",
      "principally polarized abelian surface"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1311H"
    }
  }
}