Density of potentially crystalline representations of fixed weight

Let K be a finite extension of Qₚ and let [STIX]x1D70C be a continuous, absolutely irreducible representation of its absolute Galois group with values in a finite field of characteristic p . We prove that the Galois representations that become crystalline of a fixed regular weight after an abelian extension are Zariski-dense in the generic fiber of the universal deformation ring of [STIX]x1D70C . In fact we deduce this from a similar density result for the space of trianguline representations. This uses an embedding of eigenvarieties for unitary groups into the spaces of trianguline representations as well as the corresponding density claim for eigenvarieties as a global input.