Isolating the Hodge type in moduli spaces of crystalline Galois representations

Abstract: Moduli spaces of representations of the absolute Galois group of a p-adic field play an important role in various aspects of the Langlands correspondence. In this talk I will focus on cases in which the coefficients of these representations also have characteristic p, and discuss joint work with Bao Le-Hung and Brandon Levin in which we control the singularities of these moduli spaces in several new cases. One new ingredient is a description of integral conditions, derived from Plücker coordinates on the affine Grassmannian, which cut out the locus with a specific Hodge type. This works for any ramification degree, and as an application we can extend modularity lifting theorems proved by Kisin for two dimensional Galois representations of a totally real number field, to three dimensional representations.

number theory

Audience: researchers in the topic

London number theory seminar

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