Trianguline Galois representations and Schur functors

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.

arXiv commentThe lemma cited as 4.6 turned out to be false in the generality I use it, hence the proof of one of the main results, Theorem 4.2, does not work. A new proof of all the results of Sections 1 to 6, by a different method, is given in ArXiv:2101:02189