Irreducibility of some crystalline loci with irregular Hodge-Tate weights

We show that loci of crystalline representations of G K G_K for K / Q p K/Q_p an unramified extension are irreducible when the Hodge–Tate weights are fixed and sufficiently small. This was previously known for weights in the interval [ − p , 0 ] [-p,0] and in this paper we show how that this bound can be relaxed provided the Hodge–Tate weights are sufficiently irregular at certain embeddings. This is motivated by the desire to extend the conjectures of Breuil–Mézard [Duke Math. J. 115 (2002), pp. 205–310] on loci of potentially crystalline representations to irregular weights.