Rational torsion in modular Jacobians

Preston Wake, Michigan State University

For a prime number N, Ogg's conjecture states that the torsion in the Jacobian of the modular curve X0(N)�0(�) is generated by the cusps. Mazur proved Ogg's conjecture as one of the main theorems in his "Eisenstein ideal" paper. I'll talk about a generalization of Ogg's conjecture for squarefree N and a proof using the Eisenstein ideal. This is joint work with Ken Ribet.�