Cuspidal cohomology for $GL(n)$ over a number field

TL;DR

This paper proves the nonvanishing of cuspidal cohomology for certain $GL(n)$ over a Galois number field, utilizing the structure of strongly-pure weights and foundational cohomological methods.

Contribution

It establishes the nonvanishing of cuspidal cohomology for $GL(n)$ over Galois number fields, extending previous understanding of automorphic cohomology.

Findings

Nonvanishing of cuspidal cohomology for $GL(n)$ over Galois number fields.

Use of strongly-pure weights to support cuspidal cohomology.

Application of foundational work by Borel, Labesse, and Schwermer.

Abstract

The main result of this article proves the nonvanishing of cuspidal cohomology for $GL(n)$ over a number field which is Galois over its maximal totally real subfield. The proof uses the internal structure of a strongly-pure weight that can possibly support cuspidal cohomology and the foundational work of Borel, Labesse, and Schwermer.