Towards automorphy lifting for semi-stable Galois representations

Abstract: Automorphy lifting theorems aim to show that a p-adic global Galois representation that is unramified almost everywhere and de Rham at places dividing p is associated to an automorphic representation, provided its reduction modulo p is. In the past years there has been a lot of progress in the case of polarizable representations that are crystalline at p. In the semi-stable case much less is known (beyond the ordinary case and the 2-dimensional case).

I will explain recent progress on classicality theorems for p-adic automorphic forms whose associated Galois representation is semi-stable at places dividing p. In the context of automorphy lifting problems, these results can be used to deduce the semi-stable case from the crystalline case.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar