On the images of the Galois representations attached to generic automorphic representations of GSp(4)
arXiv:1605.08020 · doi:10.2422/2036-2145.201609_016
Abstract
By making use of Langlands functoriality between GSp(4) and GL(4), we show that the images of the Galois representations attached to "genuine" globally generic automorphic representations of GSp(4) are "large" for almost every prime. Moreover, by using the notion of (n,p)-groups (introduced by Khare, Larsen and Savin) and generic Langlands functoriality from SO(5) to GL(4) we construct automorphic representations of GSp(4) such that the compatible system attached to them has large image for all primes.
arXiv commentRevised version - referees' comments added. The final version is to appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5)