Spherical varieties and p-adic families of cohomology classes

TL;DR

This paper establishes a twist-compatibility property for p-adic families of cohomology classes, enabling interpolation of classical classes across various weights and applications to Euler systems in symplectic groups.

Contribution

It proves a general twist-compatibility result for p-adic cohomology families, extending prior work and enabling new applications to Euler systems for symplectic groups.

Findings

Interpolates classical cohomology classes across different weights

Generalizes previous results on Euler systems and p-adic L-functions

Provides new applications to GSp(4) and related groups

Abstract

We prove a "twist-compatibility" result for p-adic families of cohomology classes associated to symmetric spaces. This shows that a single family of classes (lying in a finitely-generated Iwasawa module) interpolates classical cohomology classes of many different weights, including twists by Gr\"ossencharacters of possibly non-trivial infinity-type. This subsumes and generalises a number of prior results relating to Euler systems and p-adic L-functions, and we conclude with some novel applications to Euler systems for GSp(4), GSp(4) x GL(2), and GSp(4) x GL(2) x GL(2).