{
  "id": "math/0409352",
  "version": "v1",
  "published": "2004-09-20T13:42:40.000Z",
  "updated": "2004-09-20T13:42:40.000Z",
  "title": "Abelian surfaces of GL2-type as Jacobians of curves",
  "authors": [
    "Josep Gonzalez",
    "Jordi Guardia",
    "Victor Rotger"
  ],
  "comment": "To appear in Acta Arithmetica",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study the set of isomorphism classes of principal polarizations on abelian varieties of GL2-type. As applications of our results, we construct examples of curves C, C'/\\Q of genus two which are nonisomorphic over \\bar \\Q and share isomorphic unpolarized modular Jacobian varieties over \\Q ; we also show a method to obtain genus two curves over \\Q whose Jacobian varieties are isomorphic to Weil's restriction of quadratic \\Q-curves, and present examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-20T13:42:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G18",
      "14H40"
    ],
    "keywords": [
      "abelian surfaces",
      "isomorphic unpolarized modular jacobian varieties",
      "share isomorphic unpolarized modular jacobian",
      "abelian varieties",
      "weils restriction"
    ],
    "publication": {
      "doi": "10.4064/aa116-3-3",
      "journal": "Acta Arithmetica",
      "year": 2005,
      "volume": 116,
      "number": 3,
      "pages": 263
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005AcAri.116..263G"
    }
  }
}