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

Abstract

We study the $L^2$--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 $L^2$-cohomology contributing to the lowest weight part.

final version

References in corpus (1)

• Deligne-Hodge-DeRham theory with coefficients