On the Eisenstein cohomology of odd orthogonal groups

TL;DR

This paper characterizes the Eisenstein cohomology of split odd orthogonal groups over Q, identifying conditions under which Eisenstein series produce non-trivial automorphic cohomology classes.

Contribution

It provides a detailed description of residual and regular Eisenstein cohomology classes for certain automorphic representations of odd orthogonal groups.

Findings

Identifies necessary conditions for Eisenstein series to generate non-trivial cohomology classes.

Describes residual and regular Eisenstein cohomology classes for maximal parabolic subgroups.

Analyzes the role of cohomological cuspidal automorphic representations in Eisenstein cohomology.

Abstract

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes for maximal parabolic Q-subgroups in case of generic cohomological cuspidal automorphic representations of their Levi subgroups. That is, such identifying necessary conditions on these latter representations as well as on the complex parameters in order for the associated Eisenstein series to possibly yield non-trivial classes in the automorphic cohomology.