Controlling the irreducible components of some crystalline deformation rings.

For applications to modularity lifting theorems it is useful to understand the irreducible components of deformation rings parametrising crystalline representations with fixed Hodge-Tate weights. In this talk I will explain how a method Kisin used when the Hodge-Tate weights are between 0 and 1 can be extended to a larger collection of Hodge-Tate weights. This involves resolves these deformations rings using moduli spaces of objects from p-adic Hodge theory.