Kalyani Kansal will speak on

Intersections of components of Emerton-Gee stack for GL2

Let p be a fixed odd prime, and let K be a finite extension of Qp with ring of integers O_K. The Emerton-Gee stack for GL2 is a stack of (phi, Gamma)-modules of rank two. Its reduced part, X, is an algebraic stack of finite type over a finite field, and it can be viewed as a moduli stack of mod p representations of the absolute Galois group of K. The irreducible components of X are labelled in a natural way by Serre weights, which are the irreducible mod p representations of GL_2(O_K). Motivated by the conjectural categorical p-adic Langlands programme, we find representation-theoretic criteria for codimension 1 intersections of the irreducible components of X. More precisely, we show that GL_2(O_K) extensions of Serre weights are related to codimension 1 intersections of the irreducible components. We further show that the level at which the Serre weight extensions arise is related to the number of the top dimensional components in a codimension 1 intersection.