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Trianguline lifts of global mod $p$ Galois representations

Najmuddin Fakhruddin, Chandrashekhar Khare and Stefan Patrikis

Vol. 320 (2022), No. 2, 223–240

We show that under a suitable oddness condition, for p Fn 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.

Galois representations, deformations of Galois representations
Mathematical Subject Classification
Primary: 11F80
Received: 2 March 2022
Revised: 24 July 2022
Accepted: 25 August 2022
Published: 15 February 2023
Najmuddin Fakhruddin
School of Mathematics
Tata Institute of Fundamental Research
Chandrashekhar Khare
Department of Mathematics
University of California Los Angeles
Los Angeles, CA
United States
Stefan Patrikis
Department of Mathematics
Ohio State University
Columbus, OH
United States