The rational cuspidal subgroup of J₀(N)

2025/04/17 by Hwajong Yoo, Myungjun Yu, Yoo, Hwajong +1
Mathematics · #11F18 #14G05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2504.12564

openalex publication_date 2025/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a positive integer N, let J₀(N) be the Jacobian of the modular curve X₀(N). In this paper we completely determine the structure of the rational cuspidal subgroup of J₀(N) when the largest perfect square dividing N is either an odd prime power or a product of two odd prime powers. Indeed, we prove that the rational cuspidal divisor class group of X₀(N) is the whole rational cuspidal subgroup of J₀(N) for such an N, and the structure of the former group is already determined by the first author in [14].

Related

• Computing the Cuspidal Subgroup of the Modular Jacobian J_H( p )
• The rational torsion subgroup of J₀(N)
• The rational cuspidal subgroup of J₀(p²M) with M squarefree
• The rational cuspidal divisor class group of X₀(N)
• Modular unit and cuspidal divisor class groups of X₁(N)