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

2024/07/10 by Kalyani Kansal, Kansal, Kalyani, Ben Savoie +1
Physics and Astronomy · #11S99 #Black Holes and Theoretical Physics #FOS: Mathematics #Number Theory (math.NT) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.2407.07883

openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a finite unramified extension of ℚ_p with p > 3. We study the extremely non--generic irreducible components in the reduced part of the Emerton--Gee stack for GL₂. 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.

Related

• Smoothness of components of the Emerton-Gee stack for GL₂
• Functions on Irreducible Components of the Emerton-Gee Stack
• Codimension one intersections between components of the Emerton-Gee stack for GL₂
• Generic smooth representations
• Irregular loci in the Emerton-Gee stack for GL₂