{
  "id": "2106.01020",
  "version": "v1",
  "published": "2021-06-02T08:39:07.000Z",
  "updated": "2021-06-02T08:39:07.000Z",
  "title": "The rational torsion subgroup of $J_0(N)$",
  "authors": [
    "Hwajong Yoo"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "The main result of this paper is to determine the structure of the rational torsion subgroup of the modular Jacobian variety $J_0(N)$ for any positive integer $N$ up to finitely many primes. More precisely, we prove that the prime-to-$2n$ part of the rational torsion subgroup of $J_0(N)$ is equal to that of the rational cuspidal divisor class group of $X_0(N)$, where $n$ is the largest perfect square dividing $3N$. As the rational cuspidal divisor class group of $X_0(N)$ is already computed in [28], it determines the structure of the rational torsion subgroup of $J_0(N)$ up to primes dividing $2n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-02T08:39:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G05",
      "14G35"
    ],
    "keywords": [
      "rational torsion subgroup",
      "rational cuspidal divisor class group",
      "modular jacobian variety",
      "largest perfect square",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}