{
  "id": "math/0312435",
  "version": "v1",
  "published": "2003-12-23T22:01:03.000Z",
  "updated": "2003-12-23T22:01:03.000Z",
  "title": "Shimura curves embedded in Igusa's threefold",
  "authors": [
    "Victor Rotger"
  ],
  "comment": "To appear in Modular curves and Abelian varieties, Progress in Mathematics 224 Birkhauser, (2003), 263-273",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let O be a maximal order in a totally indefinite quaternion algebra over a totally real number field. In this note we study the locus Q_O of quaternionic multiplication by O in the moduli space A_g of principally polarized abelian varieties of even dimension g with particular emphasis in the two-dimensional case. We describe Q_O as a union of Atkin-Lehner quotients of Shimura varieties and we compute the number of irreducible components of Q_O in terms of class numbers of CM-fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-23T22:01:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G35"
    ],
    "keywords": [
      "shimura curves",
      "igusas threefold",
      "totally indefinite quaternion algebra",
      "totally real number field",
      "moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12435R"
    }
  }
}