{
  "id": "1303.5270",
  "version": "v1",
  "published": "2013-02-22T07:22:57.000Z",
  "updated": "2013-02-22T07:22:57.000Z",
  "title": "Algebraic points on Shimura curves of $Γ_0(p)$-type (III)",
  "authors": [
    "Keisuke Arai"
  ],
  "comment": "11 pages. arXiv admin note: substantial text overlap with arXiv:1211.0129, arXiv:1205.3596, arXiv:1202.4841",
  "categories": [
    "math.NT"
  ],
  "abstract": "In previous articles, we classified the characters associated to algebraic points on Shimura curves of $\\Gamma_0(p)$-type, and over number fields in a certain large class we showed that there are at most elliptic points on such a Shimura curve for every sufficiently large prime number $p$. In this article, we prove the non-existence of elliptic points on Shimura curves of $\\Gamma_0(p)$-type under a mild assumption. We also give an explicit example.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-22T07:22:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G05",
      "11G10",
      "11G15"
    ],
    "keywords": [
      "shimura curve",
      "algebraic points",
      "elliptic points",
      "sufficiently large prime number",
      "explicit example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.5270A"
    }
  }
}