Abstract Robin Bartlett

Robin Bartlett will speak on

Crystalline deformation rings with weights between 0 and p

Abstract: For applications to the Fontaine--Mazur conjecture and modularity lifting theorems, it is useful to have an understanding of the geometry of certain deformation spaces of p-adic Galois representations. These spaces are indexed by Hodge--Tate weights and while, for small weights, the geometry is well understood, as the weights become large far less is known. After explaining why these spaces are related to modularity lifting theorems, I will explain an extension of a method, originally applied by Kisin for weights between 0 and 1, which produces a resolution of these deformation rings via semi-linear algebra. For unramified extensions of Qp, and weights between 0 and p, this can be used to describe the irreducible components of these rings.