Rational torsion of generalised Drinfeld modular Jacobians of prime power level

2024/12/18 by Curcó-Iranzo, Mar
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2412.14313

Abstract

For a prime \mathfrakp ⊆ \mathbbF_q[T] and a positive integer r, we consider the generalised Jacobian J₀(\mathfrakn)_m of the Drinfeld modular curve X₀(\mathfrakn) of level \mathfrakn=\mathfrakp^r, with respect to the modulus~m consisting of all cusps on the modular curve. We show that the ℓ-primary part of the group J₀(\mathfrakn)_m(\mathbbF_q(T))_\rmtor[ℓ^∞] is trivial for all primes ℓ not dividing q(q²-1). Our results establish a function field analogue to those of Yamazaki--Yang for the classical case.

Related

• Rational torsion of generalised modular Jacobians of odd level
• Generalized Jacobians of modular and Drinfeld modular curves
• Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus
• The rational torsion subgroup of J₀(N)
• The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains