Norm-compatible systems of Galois cohomology classes for $GSp_6$

TL;DR

This paper constructs compatible Galois cohomology classes for the GSp_6 Shimura variety, advancing the understanding of Euler systems and p-adic L-functions in the context of automorphic Galois representations.

Contribution

It introduces a new method to build global cohomology classes compatible across levels, forming an Euler system for GSp_6-related Galois representations.

Findings

Construction of compatible cohomology classes across levels.

Establishment of elements in Iwasawa cohomology.

Derivation of p-adic L-functions via Perrin-Riou's machinery.

Abstract

We construct global cohomology classes in the middle degree cohomology of the Shimura variety of the symplectic group $GSp_6$ compatible when one varies the level at $p$. These classes are expected constituents of an Euler system for the Galois representations appearing in these cohomology groups. As an application, we show how these classes provide elements in the Iwasawa cohomology of these representations and, by applying Perrin-Riou's machinery, $p$-adic L-functions associated to them.