Abstract

In this talk, we first classify potentially semistable Galois representations of a given inertial type using some variants of Breuil-Kisin modules. Then we use this classification to study the smoothness of the map from the rigid generic fiber of the Emerton-Gee stack of potentially semistable representations to the analytification of stack of Weil-Deligne representations. Finally, as an application, we give smoothness results of the EG stack of potentially semistable representations. We also give a regularity criterion of the generic fiber of certain semistable deformation rings in terms of the mod p Galois representations.