{
  "id": "1411.1162",
  "version": "v1",
  "published": "2014-11-05T06:27:25.000Z",
  "updated": "2014-11-05T06:27:25.000Z",
  "title": "Points on Shimura curves rational over imaginary quadratic fields in the non-split case",
  "authors": [
    "Keisuke Arai"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For an imaginary quadratic field $k$ of class number $>1$, Jordan proved that there are only finitely many isomorphism classes of rational indefinite quaternion division algebras $B$ such that the associated Shimura curve has $k$-rational points and $k$ splits $B$. In this article, we study the case where $k$ does not split $B$, and obtain an analogous result by imposing a certain congruent condition on the discriminant of $B$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-05T06:27:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G05"
    ],
    "keywords": [
      "imaginary quadratic field",
      "shimura curves rational",
      "non-split case",
      "rational indefinite quaternion division algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1162A"
    }
  }
}