Codimension one intersections between components of the Emerton-Gee stack for GL₂

Let p p be a fixed odd prime, and let K K be a finite extension of Q p Q_p with ring of integers O K O_K . The Emerton-Gee stack for G L 2 GL_2 is a stack of ( φ , Γ ) (φ , Γ ) -modules. The stack, denoted X 2 X_2 , can be interpreted as a moduli stack of representations of the absolute Galois group of K K with p p -adic coefficients. The reduced part of the Emerton-Gee stack, denoted X 2 , r e d X2, red , is an algebraic stack defined over a finite field of characteristic p p and can be viewed as a moduli stack of Galois representations with mod p p coefficients. The irreducible components of X 2 , r e d X2, red are labelled in a natural way by Serre weights, which are the irreducible mod p p