{
  "id": "1202.4841",
  "version": "v2",
  "published": "2012-02-22T07:36:17.000Z",
  "updated": "2012-10-29T08:29:34.000Z",
  "title": "Algebraic points on Shimura curves of $Γ_0(p)$-type",
  "authors": [
    "Keisuke Arai",
    "Fumiyuki Momose"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this article, we classify the characters associated to algebraic points on Shimura curves of $\\Gamma_0(p)$-type, and over a quadratic field we show that there are at most elliptic points on such a Shimura curve for every sufficiently large prime number $p$. This is an analogue of the study of rational points or points over a quadratic field on the modular curve $X_0(p)$ by Mazur and one of the author (Momose). We also apply the result to a finiteness conjecture on abelian varieties with constrained prime power torsion by Rasmussen-Tamagawa.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-29T08:29:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G05"
    ],
    "keywords": [
      "shimura curve",
      "algebraic points",
      "quadratic field",
      "constrained prime power torsion",
      "sufficiently large prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.4841A"
    }
  }
}