Construction of automorphic Galois representations, II

Deformation of Outer Representations of Galois Group II

This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for...

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 ...