Quadratic torsion subgroups of modular Jacobian varieties

2019/01/27 by Yuan Ren, Ren, Yuan
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1901.09896

openalex publication_date 2019/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D be an odd square-free positive integer and C a divisor of D. For any quadratic character χ modulo C, we prove that the χ-part of the group J₀(DC)_tor of torsion points of J₀(DC) coincides with the χ-part of its cuspidal subgroup, away from those primes of bad reduction or where possible congruences between oldforms and newforms occur.

Citations

• Modular Elliptic Curves and Fermat's Last Theorem

Related

• On the torsion subgroups of the modular Jacobians
• 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