Rational torsion in modular Jacobians

Preston Wake, Michigan State University
Fine Hall 214

Meeting ID:  920 2195 5230

Passcode:    The three-digit integer that is the cube of the sum of its digits. 

For a prime number N, Ogg's conjecture states that the torsion in the Jacobian of the modular curve X_0(N) 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.