Maximal Eisenstein ideals and cuspidal subgroups of modular Jacobian varieties

2019/08/28 by Yuan Ren, Ren, Yuan
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1908.10537

openalex publication_date 2019/08/28 · openalex created_date 2019/09/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the torsion subgroup of J₀(N) over the field generated by those points in the cuspidal group, where N is an odd positive integer. We prove that, considered as Hecke modules, this group and the cuspidal subgroup are both supported at the maximal Eisenstein ideals.

Citations

• Modular Elliptic Curves and Fermat's Last Theorem

Related

• Ribet's conjecture for Eisenstein maximal ideals
• On Eisenstein ideals and the cuspidal group of J₀(N)
• Quadratic torsion subgroups of modular Jacobian varieties
• The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains
• The rational cuspidal subgroup of J₀(N)