Cuspidal cohomology for GL(n) over a number field

2024/07/15 by Darshan, Nasit, Raghuram, A.
#11F70 #11F75 #22E41 #22E55 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2407.10859

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.

Related

• Endoscopy and the cohomology of GL(n)
• Cuspidal cohomology classes for GL_n(Z)
• Cuspidal representations which are not strongly cuspidal
• Contribution of symmetric power transfers to the cuspidal cohomology of \rm GL_n
• Cuspidal ℓ-modular representations of GL_n(F) distinguished by a Galois involution