Automorphic lifts of prescribed types

Automorphic Lifts of Prescribed Types

We prove a variety of results on the existence of automorphic Galois representations lifting a residual automorphic Galois representation. We prove a result on the structure of deformation rings of local Galois representations, and deduce from this and the method of Khare and Wintenberger a result on the existence of modular lifts of specified type for Galois representations corresponding to Hi...

Potentially Crystalline Lifts of Certain Prescribed Types

We prove several results concerning the existence of potentially crystalline lifts of prescribed Hodge–Tate weights and inertial types of a given representation r : GK → GLn(Fp), where K/Qp is a finite extension. Some of these results are proved by purely local methods, and are expected to be useful in the application of automorphy lifting theorems. The proofs of the other results are global, m...

AUTOMORPHY FOR SOME l-ADIC LIFTS OF AUTOMORPHIC

We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge-Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spi...

Automorphic representations with prescribed ramification for unitary groups

Let F be a totally real number field, n a prime integer, and G a unitary group of rank n defined over F that is compact at infinity. We prove an asymptotic formula for the number of automorphic representations of G whose factors at finitely many places are prescribed up to inertia. These factors are specified by local inertial types, and the proof relies crucially on a bound on the traces of th...

Automorphy for some l-adic lifts of automorphic modl Galois representations. II