Towards a mod-$p$ Lubin-Tate theory for $\GL_2$ over totally real fields
Number Theory
2022-06-22 v1
Abstract
We show that the conjectural mod local Langlands correspondence can be realised in the mod cohomology of the Lubin-Tate towers. The proof utilizes a well known conjecture of Buzzard-Diamond-Jarvis \cite[Conj. 4.9]{BDJ10}, a study of completed cohomology of the ordinary and supersingular locus of the Shimura curves for a totally real field and of mod local Langlands correspondence as given by Emerton-Helm \cite{EmertonHelm14}. %And then we connect the completed cohomlgy with the cohomology of Lubin-Tate towers. In the case of modular curves a similar theorem was obtained by Chojecki \cite{Cho15}.
Keywords
Cite
@article{arxiv.2206.09706,
title = {Towards a mod-$p$ Lubin-Tate theory for $\GL_2$ over totally real fields},
author = {Debargha Banerjee and Vivek Rai},
journal= {arXiv preprint arXiv:2206.09706},
year = {2022}
}