The Rational Torsion Subgroup of $J_0(\mathfrak{p}^r)$
| Autor: | Ho, Sheng-Yang Kevin |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Research in the Mathematical Sciences 11 (2024), no. 4, 60 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s40687-024-00474-7 |
| Popis: | 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 $\mathcal{T}(\mathfrak{p}^r)$. Comment: 21 pages, to appear on Research in the Mathematical Sciences |
| Databáze: | arXiv |
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