Mixed Hodge complexes and L²-cohomology for local systems on ball quotients

2007/07/20 by Stefan Müller–Stach, Müller-Stach, S., Xuanming Ye +3
Mathematics · #14C25 #14F17 #14G35 #32M15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0707.3084

openalex publication_date 2007/07/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the L²--cohomology of certain local systems on non-compact arithmetic ball quotients X=Γ\backslash \B_n, in particular vanishing and non--vanishing results. We also give generalizations to higher dimensional ball quotients and study the mixed Hodge structure on the sheaf cohomology of a local system with the L²-cohomology contributing to the lowest weight part.

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