Higher Hida theory

Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program
Topic:Higher Hida theory
Speaker:Vincent Pilloni
Affiliation:Centre national de la recherche scientifique
Date:Tuesday, November 7
Time/Room:10:00am - 11:00am/S-101
Video Link:https://video.ias.edu/MotivesGaloisRepsandCohomology/2017/1107-VincentPilloni

Abstract:  In usual Hida theory, one constructs a module over weight space whose specialitzation to sufficiently regular weight is a space over classical ordinary modular forms.  The goal of higher Hida theory is to construct a perfect complex of modules over (part of) weight space whose specialization to classical *non-regular* weights is a complex which (in favorable circumstances) computes the coherent cohomology of the assoicated Shimura variety in that weight.  In this talk, we outline a construction of these complexes for GSp(4) and certain families of irregular weights.