Rational torsion points on Jacobians of modular curves

2015/04/19 by Hwajong Yoo, Yoo, Hwajong
Mathematics · #11G10 #11G18 #14G05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G10 #msc:11G18 #msc:14G05

paper · pdf · doi:10.48550/arxiv.1504.04842

arxiv created 2015/10/25 · arxiv updated 2015/10/27

Abstract

Let p be a prime greater than 3. Consider the modular curve X₀(3p) over ℚ and its Jacobian variety J₀(3p) over ℚ. Let T(3p) and C(3p) be the group of rational torsion points on J₀(3p) and the cuspidal group of J₀(3p), respectively. We prove that the 3-primary subgroups of T(3p) and C(3p) coincide unless p≡ 1 \pmod 9 and 3^(p-1)/(3) ≡ 1 \pmod p.

Related

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