Non-generic components of the Emerton-Gee stack for GL2.

Kalyani Kansal (Imperial College London)

Wednesday 6th November 16:00-17:00 Maths 311B

Abstract

Let K be an unramified extension of Qp for a prime p > 3. The reduced part of the Emerton-Gee stack for GL2 can be viewed as parameterizing two-dimensional mod p Galois representations of the absolute Galois group of K. In this talk, we will consider the extremely non-generic irreducible components of this reduced part and see precisely which ones are smooth or normal, and which have Gorenstein normalizations. We will see that the normalizations of the irreducible components admit smooth-local covers by resolution-rational schemes. We will also determine the singular loci on the components, and use these results to update expectations about the conjectural categorical p-adic Langlands correspondence. This is based on recent joint work with Ben Savoie.

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