Kalyani Kansal (Johns Hopkins University)

Abstract: 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 a p-adic Galois group. We compute criteria for codimension one intersections of the irreducible components of X. We interpret these criteria in terms of representation theory of GL2, motivated by conjectural categorical p-adic and mod p Langlands correspondence. We also give a representation-theoretic cohomological criterion for the number of top-dimensional components in a codimension one intersection.