Irreducibility of automorphic Galois representations of GL(n), n at most 5

IRREDUCIBILITY OF AUTOMORPHIC GALOIS REPRESENTATIONS OF GL(n), n AT MOST 5. FRANK CALEGARI AND TOBY GEE

Let π be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GLn(AF ), where F is a totally real field and n is at most 5. We show that for all primes l, the l-adic Galois representations associated to π are irreducible, and for all but finitely many primes l, the mod l Galois representations associated to π are also irreducible. We also show that the Lie algebras...

Most-continuous automorphic spectrum for GLn

We show that the map from minimal-parabolic pseudo-Eisenstein series to their decomposition coefficients against minimal-parabolic Eisenstein series is an isometry to its image. The argument characterizing the image is sketched, but is incomplete without characterizing the other, less-continuous parts of the spectral decomposition. Thus, we do not quite prove Plancherel for this part of the spe...

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)

Deformation of Outer Representations of Galois Group

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...