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

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.

Section 6 on the main theorem and its proof has been enhanced with more details in this revised version