Smoothness of components of the Emerton-Gee stack for

Let K K be a finite unramified extension of Q p \mathbb {Q}_p , where p > 2 p>2 . The works of Caraiani, Emerton, Gee and Savitt have constructed a moduli stack of two dimensional mod p p representations of the absolute Galois group of K K . We show that most irreducible components of this stack (including several non-generic components) are isomorphic to quotients of smooth affine schemes. We also use this quotient presentation to compute global sections on these components.