Local (\ell = p) Galois Deformation Rings

I will present joint work with V. Paškūnas and G. Böckle concerning deformation rings for mod p Galois representations of p-adic local fields. After giving a short introduction to the subject, I will explain our main result which says that framed local deformation rings are complete intersections of the “expected dimension”, and which gives a classification of their irreducible components in terms of a determinant map. I will explain some of the ingredients that go into our proof, which involves work on pseudo-deformations by Böckle--Juschka, and moduli spaces of representations with fixed pseudo-character. If time permits I will discuss an application to density of crystalline points in deformation spaces.