Kisin showed that the generic fibers of potentially semi-stable (framed) deformation rings of p-adic Galois representations valued in GL_n are generically smooth, and he computed their dimensions.  I will explain how to extend these results to Galois representations valued in an arbitrary connected reductive group G.  If time permits, I will give an example showing that the corresponding schemes can have singular components.  The key tool is the geometry of the nilpotent cone.