Lifting trianguline Galois representations along isogenies

2021/01/06 by Conti, Andrea
#11F33 #11F80 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2101.02189

Abstract

Given a central isogeny π\colon G→ H of connected reductive \mathbb Q_p-groups, and a local Galois representation ρ valued in H(\mathbb Q_p) that is trianguline in the sense of Daruvar, we study whether a lift of ρ along π is still trianguline. We give a positive answer under weak conditions on the Hodge--Tate--Sen weights of ρ, and the assumption that the trianguline parameter of ρ can be lifted along π. This is an analogue of the results proved by Wintenberger, Conrad, Patrikis, and Hoang Duc for p-adic Hodge-theoretic properties of ρ. We describe a Tannakian framework for all such lifting problems, and we reinterpret the existence of a lift with prescribed local properties in terms of the simple connectedness of a certain pro-semisimple group. While applying this formalism to the case of trianguline representations, we extend a result of Berger and Di Matteo on triangulable tensor products of B-pairs.

Related

• Non-regular trianguline representations
• Modularity of trianguline Galois representations
• Trianguline Galois representations and Schur functors
• On triangulable tensor products of B-pairs and trianguline\n representations
• Eigenvarieties over CM fields and trianguline representations