Rational torsion of generalised modular Jacobians of odd level

Mar Curcó Iranzo

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arXiv · 2112.03741

Rational torsion of generalised modular Jacobians of odd level

Mar Curcó Iranzo

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Abstract

We consider the generalised Jacobian $J_{0}(N)_{\mathbf{m}}$ of the modular curve $X_{0}(N)$ of level $N$, with respect to the modulus $\mathbf{m}$ consisting of all cusps on the modular curve. When $N$ is odd, we determine the group structure of the rational torsion $J_{0}(N)_{\mathbf{m}}(\mathbb{Q})_{tor}$ up to $2$-primary and $l$-primary parts for any prime $l$ dividing $N$. Our results extend those of Wei--Yamazaki for squarefree levels and Yamazaki--Yang for prime-power levels.

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Mar Curcó Iranzo. 2021-12-07. Rational torsion of generalised modular Jacobians of odd level. https://arxiv.org/abs/2112.03741

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