2024 Program for Women+ and Mathematics

Abstract: The Emerton-Gee stack is a stack of etale $\phi$ modules, and can be viewed as a stack of p-adic representations for the Galois group of a finite extension $K$ of $Qp$. In this talk, we will introduce the stack and talk about its role in the conjecture by Emerton, Gee and Hellmann on categorical p-adic Langlands. We will focus attention on the reduced part of the stack for GL2, which can be viewed as parametrizing two-dimensional representations with mod p coefficients, and discuss various questions and results motivated by this conjectural categorical correspondence.