Mixed Hodge complexes and L^2-cohomology for local systems on ball quotients

Details Mixed Hodge complexes and L^2-cohomology for local systems on ball quotients Mixed Hodge complexes and L^2-cohomology for local systems on ball quotients

2007-07-20

arxiv.org/abs/0707.3084v6

Mathematics

Algebraic Geometry

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Scientific paper

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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