Trianguline lifts of global mod $p$ Galois representations

Abstract

We show that under a suitable oddness condition, irreducible mod $p$ representations of the absolute Galois group of an arbitrary number field 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 variants of this result for representations valued in connected reductive groups.

The main theorem is now phrased in a more natural degree of generality, for any number field. Comments welcome

References in corpus (4)

• Une interprétation modulaire de la variété trianguline
• Extended eigenvarieties for overconvergent cohomology
• On the image of complex conjugation in certain Galois representations
• Minimally Ramified Deformations when $\ell \ne p$