{
  "id": "math/0510063",
  "version": "v1",
  "published": "2005-10-04T06:22:08.000Z",
  "updated": "2005-10-04T06:22:08.000Z",
  "title": "Arithmetic of the [19,1,1,1,1,1] fibration",
  "authors": [
    "Matthias Schuett",
    "Jaap Top"
  ],
  "comment": "8 pages, plain text",
  "journal": "Comm. Math. Univ. St. Pauli 55, 1 (2006), 9-16",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "This paper studies the arithmetic of the extremal elliptic K3 surface with configuration of singular fibres [19,1,1,1,1,1]. We give a model over Q such that the Neron Severi group is generated by divisors over Q, and we describe the local Hasse-Weil zeta-functions in terms of a modular form of weight 3. Furthermore we verify the Tate conjecture for the reduction at 3 and comment on a conjecture of T. Shioda concerning the similarity of the lattice of transcendental cycles and a lattice resulting from supersingular reduction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-10-04T06:22:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G25",
      "14J27",
      "14J28"
    ],
    "keywords": [
      "arithmetic",
      "extremal elliptic k3 surface",
      "local hasse-weil zeta-functions",
      "neron severi group",
      "supersingular reduction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10063S"
    }
  }
}