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arXiv · 2504.12564

The rational cuspidal subgroup of J_0(N)

Hwajong Yoo·Myungjun Yu
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Abstract

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].

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Hwajong Yoo, Myungjun Yu. 2025-04-17. The rational cuspidal subgroup of J_0(N). https://arxiv.org/abs/2504.12564

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