Some mixed Hodge structure on l^2-cohomology of covering of Kähler manifolds

Abstract

We give methods to compute l^2-cohomology groups of a covering manifolds obtained by removing pullback of a (normal crossing) divisor to a covering of a compact Kähler manifold. We prove that in suitable quotient categories, these groups admit natural mixed Hodge structure whose graded pieces are given by expected Gysin maps.

40 pages. This revised version will be published in Mathematische Annalen