{
  "id": "math/0406625",
  "version": "v2",
  "published": "2004-06-30T17:19:25.000Z",
  "updated": "2005-02-22T16:10:10.000Z",
  "title": "Failure of the Hasse principle for Atkin-Lehner quotients of Shimura curves over \\Q",
  "authors": [
    "V. Rotger",
    "A. Skorobogatov",
    "A. Yafaev"
  ],
  "comment": "To appear in Moscow Math. Journal. Completely revised and improved version",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We show how to construct counter-examples to the Hasse principle over the field of rational numbers on Atkin-Lehner quotients of Shimura curves and on twisted forms of Shimura curves by Atkin-Lehner involutions. A particular example is the quotient of the Shimura curve X attached to the indefinite rational quaternion algebra of discriminant 23*107 by the Atkin-Lehner involution w107. The quadratic twist of X by Q(sqrt{-23}) with respect to this involution is also a counter-example to the Hasse principle over Q.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-02-22T16:10:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18"
    ],
    "keywords": [
      "shimura curve",
      "hasse principle",
      "atkin-lehner quotients",
      "indefinite rational quaternion algebra",
      "atkin-lehner involution w107"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6625R"
    }
  }
}