On the torsion subgroups of the modular Jacobians

2017/09/07 by Yuan Ren, Ren, Yuan
Mathematics · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1709.02088

Abstract

For any positive integer N, we prove that the rational torsion subgroup of J₀(N) agrees with its rational cuspidal subgroups up to a factor of 6N∏_{p| N}(p²-1). Moreover, for modular Jacobians of the form J₀(DC) with D a positive square-free integer and C any positive divisor of D, we prove that the ψ-part of the torsion subgroup of J₀(DC) agrees with the ψ-part of its cuspidal subgroup up to a factor of 6D∏_{p| D}(p²-1), where ψ is any quadratic character of conductor dividing C.

Related

• Quadratic torsion subgroups of modular Jacobian varieties
• The rational torsion subgroup of J₀(N)
• Computing the Cuspidal Subgroup of the Modular Jacobian J_H( p )
• Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus
• Rational torsion of generalised modular Jacobians of odd level