Trianguline Galois representations and Schur functors

TL;DR

This paper proves that the property of being trianguline for B-pairs is preserved under Schur functors, extending previous work, and explores implications for Galois representations and deformation spaces in the context of the Langlands program.

Contribution

It establishes an equivalence of trianguline property under Schur functors and connects this to deformation spaces and congruence loci in the Langlands framework.

Findings

Trianguline property is preserved under Schur functors.

Derived consequences for local Galois representations and Langlands dual groups.

Attached maps between deformation spaces and studied congruence loci.

Abstract

Given a $B$-pair $W$ and a Schur functor $S$, we show under some general assumptions that $W$ is trianguline if and only if $S(W)$ is. This is an extension of earlier work of Di Matteo. We derive some consequences on the behavior of local Galois representations under morphisms of Langlands dual groups. We attach to a Schur functor a map between the trianguline deformation spaces defined by Hellmann, and we study congruence loci on the Hecke-Taylor-Wiles varieties constructed by Breuil, Hellmann and Schraen for unitary groups.