Higher Hida theory and p-adic L-functions for GSp4

Abstract

We use the “higher Hida theory” recently introduced by the second author to p-adically interpolate periods of nonholomorphic automorphic forms for ${\mathrm{GSp}}_4$, contributing to coherent cohomology of Siegel threefolds in positive degrees. We apply this new method to construct p-adic L-functions associated to the degree-4 (spin) L-function of automorphic representations of ${\mathrm{GSp}}_4$, and the degree-8 L-function of ${\mathrm{GSp}}_4\times {\mathrm{GL}}_2$.