Density of automorphic points in deformation rings of polarized global Galois representations
Density of automorphic points in deformation rings of polarized global Galois representations
Conjecturally, the Galois representations that are attached to essentially self-dual regular algebraic cuspidal automorphic representations are Zariski-dense in a polarized Galois deformation ring. We prove new results in this direction in the context of automorphic forms on definite unitary groups over totally real fields. This generalizes the infinite fern argument …