RATIONAL TORSION ON THE GENERALIZED JACOBIAN OF A MODULAR CURVE WITH CUSPIDAL MODULUS

Abstract

We consider the generalized Jacobian (J) over tilde (0) (N) of a modular curve X-0 (N) with respect to a reduced divisor given by the sum of all cusps on it. When N is a power of a prime >= 5, we exhibit that the group of rational torsion points (J) over tilde (0) (N) (Q)(Tor) tends to be much smaller than the classical Jacobian.