We give methods to compute l 2 −cohomology groups of a covering manifold obtained by removing the 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 the expected Gysin maps.

Let V be a projective manifold, dimV ≥ 2. Let Z be an open subset in V which is pseudoconcave (see [1] Theorem Let V be a projective manifold, dimV ≥ 2. Let U be an open subset in V such that V \Ū is pseudoconcave in the sense of Andreotti and the boundary of U is connected. Let H be the maximal compact reduced divisor in U (see [3]). Assume meromorphic functions on V \Ū are rationals. Let F → V be a holomorphic vector bundle. Then any meromorphic section of F defined on a connected neighborhood W of ∂U extends as a meromorphic section of F over U . Moreover if that section is holomorphic on W , then its extension is holomorphic on U \H.Proof In the proof of theorem 3.2.4 of [3] line 34, use the hypothesis that meromorphic functions on V \Ū are rationals instead of using theorem 3.2.1.The second corrected version works for general pseudoconcave domains.The online version of the original article can be found under

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