Smoothness of components of the Emerton-Gee stack for 𝐺𝐿₂

Guzman, Anthony; Kansal, Kalyani; Kountouridis, Iason; Savoie, Ben; Wang, Xiyuan

doi:10.1090/tran/9088

Smoothness of components of the Emerton-Gee stack for $\operatorname {GL}_2$
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by Anthony Guzman, Kalyani Kansal, Iason Kountouridis, Ben Savoie and Xiyuan Wang;

Trans. Amer. Math. Soc. 378 (2025), 67-115

DOI: https://doi.org/10.1090/tran/9088

Published electronically: October 23, 2024

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Abstract:

Let $K$ be a finite unramified extension of $\mathbb {Q}_p$, where $p>2$. The works of Caraiani, Emerton, Gee and Savitt have constructed a moduli stack of two dimensional mod $p$ representations of the absolute Galois group of $K$. We show that most irreducible components of this stack (including several non-generic components) are isomorphic to quotients of smooth affine schemes. We also use this quotient presentation to compute global sections on these components.

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