Endoscopy and cohomology of a quasi-split U(4)

2014/08/31 by Simon Marshall, Marshall, Simon
Mathematics · #11F70 #11F75 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1409.0239

openalex publication_date 2014/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove asymptotic upper bounds for the L² Betti numbers of the locally symmetric spaces associated to a quasi-split U(4). These manifolds are 8-dimensional, and we prove bounds in degrees 2 and 3, with the behaviour in the other degrees being well understood. In degree 3, we conjecture that these bounds are sharp. Our main tool is the endoscopic classification of automorphic representations of U(N) by Mok.

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