On the Eisenstein functoriality in cohomology for maximal parabolic subgroups

TL;DR

This paper extends Scholze's topological method for constructing cohomology classes on arithmetic quotients of symmetric spaces, broadening its applicability to more cases and to the cohomology of local systems in the complex setting.

Contribution

It generalizes Scholze's construction beyond initial cases and applies it to the cohomology of local systems in complex symmetric spaces.

Findings

Extended the construction to more cases of maximal parabolic subgroups.

Applied the method to cohomology of local systems in the complex case.

Provided new tools for understanding cohomology in arithmetic geometry.

Abstract

In his paper, 'On torsion in the cohomology of locally symmetric varieties', Peter Scholze has introduced a new, purely topological method to construct the cohomology classes on arithmetic quotients of symmetric spaces of rational reductive groups originating from the cohomology of the similar quotients of Levi subgroups of maximal parabolic subgroups. We extend this construction beyond the cases he considers, and, in the complex case, to the cohomology of local systems.