Non-generic components of the Emerton-Gee stack for GL$_2$

Abstract: Let $K$ be an unramified extension of $\mathbb{Q}_p$ for a prime p > 3. The reduced part of the Emerton-Gee stack for $\mathrm{GL}_2$ 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 or Cohen-Macaulay normalizations, as well as determine their singular loci. We will see some consequences of this study for the conjectural categorical p-adic Langlands correspondence. This is based on recent joint work with Ben Savoie.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html