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arXiv · 2407.07883

Non-generic components of the Emerton-Gee stack for $\mathrm{GL}_2$

Kalyani Kansal·Ben Savoie
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Abstract

Let $K$ be a finite unramified extension of $\mathbb{Q}_p$ with $p > 3$. We study the extremely non--generic irreducible components in the reduced part of the Emerton--Gee stack for $\mathrm{GL}_2$. We show precisely which irreducible components are smooth, which are normal, and which have Gorenstein normalizations. We show that the normalizations of the irreducible components admit smooth--local covers by resolution--rational schemes. We also determine the singular loci on the components, and use our results to update expectations about the conjectural categorical $p$--adic Langlands correspondence.

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Kalyani Kansal, Ben Savoie. 2025-03-24. Non-generic components of the Emerton-Gee stack for $\mathrm{GL}_2$. https://arxiv.org/abs/2407.07883

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