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arXiv · 1502.01571

On Eisenstein ideals and the cuspidal group of $J_0(N)$

Hwajong Yoo
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Abstract

Let $\mathcal{C}_N$ be the cuspidal subgroup of the Jacobian $J_0(N)$ for a square-free integer $N>6$. For any Eisenstein maximal ideal $\mathfrak{m}$ of the Hecke ring of level $N$, we show that $\mathcal{C}_N[\mathfrak{m}]\neq 0$. To prove this, we calculate the index of an Eisenstein ideal $\mathcal{I}$ contained in $\mathfrak{m}$ by computing the order of a cuspidal divisor annihilated by $\mathcal{I}$.

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Hwajong Yoo. 2015-10-25. On Eisenstein ideals and the cuspidal group of $J_0(N)$. https://arxiv.org/abs/1502.01571

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