Irregular loci in the Emerton-Gee stack for GL_2
Number Theory
2023-09-26 v1
Abstract
Let K/Q_p be unramified. Inside the Emerton-Gee stack X_2, 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.
Cite
@article{arxiv.2309.13665,
title = {Irregular loci in the Emerton-Gee stack for GL_2},
author = {Rebecca Bellovin and Neelima Borade and Anton Hilado and Kalyani Kansal and Heejong Lee and Brandon Levin and David Savitt and Hanneke Wiersema},
journal= {arXiv preprint arXiv:2309.13665},
year = {2023}
}
Comments
36 pages