The Rational Torsion Subgroup of $J_0(\mathfrak{p}^r)
Research in the Mathematical Sciences 11 (2024), no. 4, 60 Let $\mathfrak{n} = \mathfrak{p}^r$ be a prime power ideal of $\mathbb{F}_q[T]$ with $r \geq 2$. We study the rational torsion subgroup $\mathcal{T}(\mathfrak{p}^r)$ of the Drinfeld modular Jacobian $J_0(\mathfrak{p}^r)$. We prove that the p...
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Zusammenfassung: | Research in the Mathematical Sciences 11 (2024), no. 4, 60 Let $\mathfrak{n} = \mathfrak{p}^r$ be a prime power ideal of
$\mathbb{F}_q[T]$ with $r \geq 2$. We study the rational torsion subgroup
$\mathcal{T}(\mathfrak{p}^r)$ of the Drinfeld modular Jacobian
$J_0(\mathfrak{p}^r)$. We prove that the prime-to-$q(q-1)$ part of
$\mathcal{T}(\mathfrak{p}^r)$ is equal to that of the rational cuspidal divisor
class group $\mathcal{C}(\mathfrak{p}^r)$ of the Drinfeld modular curve
$X_0(\mathfrak{p}^r)$. As we completely computed the structure of
$\mathcal{C}(\mathfrak{p}^r)$, it also determines the structure of the
prime-to-$q(q-1)$ part of $\mathcal{T}(\mathfrak{p}^r)$. |
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DOI: | 10.48550/arxiv.2404.00738 |