Towards local-global compatibility for Hilbert modular forms of low weight

TL;DR

This paper establishes new instances of local-global compatibility for Galois representations linked to low-weight Hilbert modular forms, advancing understanding in the Langlands program and modularity lifting.

Contribution

It proves new cases of local-global compatibility specifically for Galois representations of Hilbert modular forms with partial weight one.

Findings

New cases of local-global compatibility proved

Enhanced understanding of Galois representations for low-weight forms

Progress in the Langlands correspondence for Hilbert modular forms

Abstract

We prove some new cases of local--global compatibility for the Galois representations associated to Hilbert modular forms of low weight (that is, partial weight one).