Pseudorepresentations and the Eisenstein ideal

Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program
Topic:Pseudorepresentations and the Eisenstein ideal
Speaker:Preston Wake
Affiliation:University of California, Los Angeles
Date:Thursday, November 9
Time/Room:10:00am - 11:00am/S-101
Video Link:https://video.ias.edu/MotivesGaloisRepsandCohomology/2017/1109-PrestonWake

Abstract:  In his ladmark 1976 paper "Modular curves and the Eisenstein ideal", Mazur studied congruences modulo p between cusp forms and an Eisenstein series of weight 2 and prime level N. We use deformation theory of pseudorepresentations to study the corresponding Hecke algebra. We will discuss how this method can be used to refine Mazur's results, quantifying the number of Eisenstein congruences.  We'll also discuss some partial results in the composite-level case.  This is joint work with Carl Wang-Erickson.