Automorphic realization of residual Galois representations

Automorphic Realization of Residual Galois Representations

The “Galois representations” of the title are modular representations ρ of the Galois groups of a number field F , and the ”automorphic realization” of the title refers to obtaining these representations as constituents of Galois representations attached to automorphic representations of general linear groups over F . The present article refines the moduli-theoretic arguments of [HST] to show t...

Galois Representations and Automorphic Forms (MasterMath)

The Conjectural Connections between Automorphic Representations and Galois Representations

We state conjectures on the relationships between automorphic representations and Galois representations, and give evidence for them.

Deformations of Polarized Automorphic Galois Representations and Adjoint Selmer Groups

We prove the vanishing of the geometric Bloch–Kato Selmer group for the adjoint representation of a Galois representation associated to regular algebraic polarized cuspidal automorphic representations under an assumption on the residual image. Using this, we deduce that the localization and completion of a certain universal deformation ring for the residual representation at the characteristic ...

Automorphic Galois representations and the cohomology of Shimura varieties

The first part of this report describes the class of representations of Galois groups of number fields that have been attached to automorphic representations. The construction is based on the program for analyzing cohomology of Shimura varieties developed by Langlands and Kottwitz. Using p-adic methods, the class of Galois representations obtainable in this way can be expanded slightly; the lin...