Endoscopic congruences modulo adjoint L-values for GSp(4)

Abstract

We establish the existence of congruences between a fixed endoscopic, globally generic, cuspidal automorphic representation Π of $\mathrm{GSp}(4)$ of square-free conductor and stable cuspidal automorphic representations of the same weight modulo certain prime factors of the value at 1 of the adjoint L-function of Π, normalized by a suitable period.