Abstract

Abstract. Let $X$ be a complex projective manifold, $D\subset X$ a normal crossing divisor and $U=X\setminus D$ the complement. It is well known that $H^k(U)$ has a mixed Hodge structure with weights $\ge k$ and that the lowest weight part comes from the restriction $H^k(X)\to H^k(U)$. This result can be generalized for coefficient systems underlying a variation of Hodge structure. In the talk I explain how mixed Hodge modules make the proof very easy. This reports on research done jointly with Morihiko Saito.