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

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

2010-06-14

arxiv.org/abs/1006.2784v2

Mathematics

Complex Variables

27 pages, section 2.4.5 corrected (a real structure for torsion theory is stated), some typos corrected

Scientific paper

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 K\"ahler manifold. We prove that in suitable quotient categories, these
groups admit natural mixed Hodge structure whose graded pieces are given by
expected Gysin maps.

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