Abstract:Let $K / \mathbb{Q}_p$ be a finite unramified extension, and let $\mathcal{X}_n$ denote the Emerton-Gee stack parametrizing étale $(\varphi,\Gamma_K)$-modules of rank $n$. It is known since the work of Emerton-Gee that the irreducible components of the reduced special fiber of $\mathcal{X}$ are labeled by Serre weights $\sigma$ of $\operatorname{GL}_n(k)$. If such a component is denoted $\mathcal{X}(\sigma)$, we prove that $\mathcal{O}(\mathcal{X}(\sigma)) \cong \mathbb{F}[x_1,x_2,\dots,x_{n-1},x_n^{\pm 1}]$ when $\sigma$ is sufficiently generic.
From: Eivind Otto Hjelle [view email]
[v1]
Wed, 31 May 2023 19:30:53 UTC (45 KB)
[v2]
Fri, 6 Sep 2024 23:24:42 UTC (47 KB)
[v3]
Thu, 25 Jun 2026 03:02:30 UTC (49 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。