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arXiv · 1512.00586

The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains

Mihran Papikian·Fu-Tsun Wei
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Abstract

Let $\frak{n}$ be a square-free ideal of $\mathbb{F}_q[T]$. We study the rational torsion subgroup of the Jacobian variety $J_0(\frak{n})$ of the Drinfeld modular curve $X_0(\frak{n})$. We prove that for any prime number $\ell$ not dividing $q(q-1)$, the $\ell$-primary part of this group coincides with that of the cuspidal divisor class group. We further determine the structure of the $\ell$-primary part of the cuspidal divisor class group for any prime $\ell$ not dividing $q-1$.

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Mihran Papikian, Fu-Tsun Wei. 2015-12-04. The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains. https://arxiv.org/abs/1512.00586

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