Some norm relations of the Eisenstein classes of GSp(4)

TL;DR

This paper constructs a system of Galois cohomology classes related to the p-adic L-function of GSp(4), using elliptic polylogarithm and cohomology of Siegel threefolds, advancing number theory and algebraic geometry.

Contribution

It introduces a novel norm compatible system of Galois cohomology classes linked to GSp(4) L-functions, utilizing elliptic polylogarithm and cohomological techniques.

Findings

Construction of norm compatible Galois cohomology classes.

Connection to conjectural degree four p-adic L-function.

Application of elliptic polylogarithm in cohomology.

Abstract

We construct a norm compatible system of Galois cohomology classes in the cyclotomic extension of the field of rationnals giving rise (conjecturally) to the degree four p-adic L-function of the symplectic group GSp(4). These classes are defined as cup products of torsion sections of the elliptic polylogarithm pro-sheaf. We rely on the norm compatibility of the elliptic polylogarithm and on some weight computations in the cohomology of Siegel threefolds.