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

Stefan Müller-Stach, Xuanming Ye, Kang Zuo

Number 21
Authors Xuanming Ye
Kang Zuo
Stefan Müller-Stach
Year 2011

We study the $L^2$--cohomology of certain local systems on non-compact arithmetic ball quotients $X=\Gamma \backslash \B_n$, 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 $L^2$-cohomology contributing to the lowest weight part.

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