Spring 2019 Schedule:

May 10:  Preston Wake (IAS)

Title: Tame derivatives and the Eisenstein ideal

Abstract: As was made famous by Mazur, the mod-5 Galois representation associated to the elliptic curve $X_0(11)$ is reducible. In fact, the mod-25 Galois representation is also reducible. We will talk about this kind of extra reducibility phenomenon, and how its related, on one hand, to a ‘tame deriviative’ of an L-function, and on the other hand, to an algebraic invariant. This type of relation is predicted by the Bloch-Kato conjecture. This is a joint work with Akshay Venkatesh.