Generalized Jacobians of modular and Drinfeld modular curves

2018/02/04 by Wei, Fu-Tsun, Yamazaki, Takao
#11F03 #11G09 (11G18 #14G35) #14H40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1802.01066

Abstract

We consider the generalized Jacobian \widetildeJ of the modular curve X₀(N) of level N with respect to a reduced divisor consisting of all cusps. Supposing N is square free, we explicitly determine the structure of the ℚ-rational torsion points on \widetildeJ up to 6-primary torsion. The result turns out to be very different from the case of prime power level previously studied by Yang and the second author. We also obtain an analogous result for Drinfeld modular curves. Our proof relies on similar results for classical Jacobians due to Ohta, Papikian and the first author. We also discuss the Hecke action on \widetildeJ and its Eisenstein property.

Related

• Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus
• Rational torsion of generalised Drinfeld modular Jacobians of prime power level
• Rational torsion of generalised modular Jacobians of odd level
• The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains
• Torsion points on modular curves and Galois theory