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

S. Müller-Stach; X. Ye; K. Zuo

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

Algebraic Geometry 2014-10-28 v6 Number Theory

Authors: S. Müller-Stach , X. Ye , K. Zuo

Abstract

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.

Keywords

mixed Hodge complexes L^2-cohomology local systems ball quotients arithmetic ball quotients Hodge structure sheaf cohomology

Cite

@article{arxiv.0707.3084,
  title  = {Mixed Hodge complexes and L^2-cohomology for local systems on ball quotients},
  author = {S. Müller-Stach and X. Ye and K. Zuo},
  journal= {arXiv preprint arXiv:0707.3084},
  year   = {2014}
}

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

Abstract

Keywords

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