The rational cuspidal subgroup of J_0(N)
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913797076156416 |
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| author | Yoo, Hwajong Yu, Myungjun |
| author_facet | Yoo, Hwajong Yu, Myungjun |
| contents | For a positive integer $N$, let $J_0(N)$ be the Jacobian of the modular curve $X_0(N)$. In this paper we completely determine the structure of the rational cuspidal subgroup of $J_0(N)$ when the largest perfect square dividing $N$ is either an odd prime power or a product of two odd prime powers. Indeed, we prove that the rational cuspidal divisor class group of $X_0(N)$ is the whole rational cuspidal subgroup of $J_0(N)$ for such an $N$, and the structure of the former group is already determined by the first author in [14]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_12564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The rational cuspidal subgroup of J_0(N) Yoo, Hwajong Yu, Myungjun Number Theory Algebraic Geometry 11F18, 14G05 For a positive integer $N$, let $J_0(N)$ be the Jacobian of the modular curve $X_0(N)$. In this paper we completely determine the structure of the rational cuspidal subgroup of $J_0(N)$ when the largest perfect square dividing $N$ is either an odd prime power or a product of two odd prime powers. Indeed, we prove that the rational cuspidal divisor class group of $X_0(N)$ is the whole rational cuspidal subgroup of $J_0(N)$ for such an $N$, and the structure of the former group is already determined by the first author in [14]. |
| title | The rational cuspidal subgroup of J_0(N) |
| topic | Number Theory Algebraic Geometry 11F18, 14G05 |
| url | https://arxiv.org/abs/2504.12564 |