The Rational Torsion Subgroup of J₀(pʳ)

Let n=pʳ be a prime-power ideal of Fq[T] with r≥ 2. We study the rational torsion subgroup T(pʳ) of the Drinfeld modular Jacobian J₀(pʳ). We prove that the prime-to-$q(q-1)$ part of T(pʳ) is equal to that of the rational cuspidal divisor class group C(pʳ) of the Drinfeld modular curve X₀(pʳ). As we completely computed the structure of C(pʳ), it also determines the structure of the prime-to-$q(q-1)$ part of T(pʳ).