Trianguline lifts of global mod $p$ Galois representations

Najmuddin Fakhruddin, Chandrashekhar Khare and Stefan Patrikis

Vol. 320 (2022), No. 2, 223–240

DOI: 10.2140/pjm.2022.320.223

Abstract

We show that under a suitable oddness condition, for $p{\gg }_{F}n$ irreducible $n$-dimensional mod $p$ representations of the absolute Galois group of an arbitrary number field $F$ have characteristic zero lifts which are unramified outside a finite set of primes and trianguline at all primes of $F$ dividing $p$. We also prove a variant of this result under some extra hypotheses for representations into connected reductive groups.

Keywords

Galois representations, deformations of Galois representations

Mathematical Subject Classification

Primary: 11F80

Milestones

Received: 2 March 2022

Revised: 24 July 2022

Accepted: 25 August 2022

Published: 15 February 2023