Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations

Abstract

AbstractLet be a smooth, separated, geometrically connected scheme defined over a number field and a system of semisimple ‐adic representations of the étale fundamental group of such that for each closed point of , the specialization is a compatible system of Galois representations under mild local conditions. For almost all , we prove that any type A irreducible subrepresentation of is residually irreducible. When is totally real or CM, , and is the compatible system of Galois representations of attached to a regular algebraic, polarized, cuspidal automorphic representation of , for almost all , we prove that is (i) irreducible and (ii) residually irreducible if in addition .