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Rational torsion in modular Jacobians

Joint PU/IAS Number Theory

Rational torsion in modular Jacobians

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Preston Wake, Michigan State University

Meeting ID:听 920 2195 5230

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

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.

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