Lecture 3: Dimensions of deformation rings and generic unobstructedness
Abstract: This lecture will talk about deformation rings of Galois representations as defined by Barry Mazur. Their spectra are moduli spaces of Galois representations. These moduli spaces provides a context for the study of a classical conjecture of Leopoldt. I will indicate how automorphy lifting techniques give rather complete information about these moduli spaces in the self-dual case, while in the non-self-dual case, the corresponding moduli spaces are still shrouded in mystery. It is the latter case which is relevant to Leopoldt's conjecture which postulates a dimension formula for these spaces.
11.30 Srinivasa Ramanujan Lecture