Breuil-Mezard identities in moduli spaces of Breuil-Kisin modules

Abstract: The Breuil-Mezard conjectures predicts relations between certain cycles in the moduli space of mod p Galois representations, in terms of the representation theory of GLn(Fq).

In this talk I will consider the special case where the cycles in question come from two dimensional crystalline representations with small Hodge-Tate weights. Under these assumptions I will explain how the topological aspects of these identities can be obtained from analagous identities appearing, first inside the affine Grassmannian, and then in moduli spaces of Breuil-Kisin modules.

algebraic geometryalgebraic topologygroup theorynumber theoryrepresentation theory

Audience: researchers in the discipline

Queen Mary University of London Algebra and Number Theory Seminar