Erratum to "On the cuspidal cohomology of $S$-arithmetic subgroups of reductive groups over number fields "

TL;DR

This paper corrects a mistake in a previous mathematical work on the cuspidal cohomology of S-arithmetic subgroups of reductive groups over number fields, ensuring the accuracy of the original results.

Contribution

It provides a necessary correction to a foundational paper in the field, clarifying the mathematical understanding of cuspidal cohomology in this context.

Findings

Correction of a key mistake in the original paper

Clarification of the properties of cuspidal cohomology

Strengthening the validity of previous results

Abstract

We correct a mistake in the paper "On the cuspidal cohomology of $S$-arithmetic subgroups of reductive groups over number fields " by A. Borel, J.-P. Labesse, J. Schwermer that appeared in Compositio Mathematica, 102 (1996), 1-40.