Irregular loci in the Emerton-Gee stack for GL₂

2023/09/24 by Rebecca Bellovin, Neelima Borade, Bellovin, Rebecca +13
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2309.13665

Abstract

Let K/Q_p be unramified. Inside the Emerton-Gee stack X₂, one can consider the locus of two-dimensional mod p representations of the absolute Galois group of K having a crystalline lift with specified Hodge-Tate weights. We study the case where the Hodge-Tate weights are irregular, which is an analogue for Galois representations of the partial weight one condition for Hilbert modular forms. We prove that if the gap between each pair of weights is bounded by p (the irregular analogue of a Serre weight), then this locus is irreducible. We also establish various inclusion relations between these loci.

Related

• Irreducibility of some crystalline loci with irregular Hodge--Tate weights
• Inclusions between p-bounded crystalline loci in dimension two
• Extremal weights and a tameness criterion for mod p Galois representations
• On two dimensional weight two odd representations of totally real fields
• Schémas en groupes et poids de Diamond-Serre