The Rational Torsion Subgroup of $J_0({\mathfrak{p}}^r)$

Abstract

Let $\mathfrak{n}={\mathfrak{p}}^r$ be a prime power ideal of ${\mathbb{F}}_q[T]$ with $r\ge 2$. 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 $\mathcal{T}({\mathfrak{p}}^r)$.

21 pages, to appear on Research in the Mathematical Sciences

References in corpus (1)

• On the Rational Cuspidal Divisor Class Groups of Drinfeld Modular Curves $X_0({\mathfrak{p}}^r)$