On distribution relations of polylogarithmic Eisenstein classes

TL;DR

This paper extends classical distribution relations of Eisenstein classes on modular curves to higher genus Siegel modular varieties, providing an adelic refinement that broadens understanding of their cohomological properties.

Contribution

It introduces an adelic refinement of distribution relations for Eisenstein cohomology classes on Siegel modular varieties of arbitrary genus, generalizing classical results.

Findings

Distribution relations hold for integral Eisenstein cohomology classes.

Adelic refinement of these relations is established.

Generalization from modular curves to higher genus varieties.

Abstract

We show that for Siegel modular varieties of arbitrary genus, the natural distribution relations satisfied by certain integral Eisenstein cohomology classes defined by Kings admit an adelic refinement. This generalizes the classical relations for Siegel units on modular curves.