Filtered perverse complexes

Abstract

We introduce the notion of filtered perversity of a filtered differential complex on a complex analytic manifold X, without any assumptions of coherence, with the purpose of studying the connection between the pure Hodge modules and the L2-complexes. We show that if a filtered differential complex (M•, F•) is filtered perverse then DR-1 (M•, F•) is isomorphic to a filtered D-module; a coherence assumption on the cohomology of (M•, F•) implies that, in addition, this D-module is holonomic. We show the converse: the de Rham complex of a holonomic Cohen-Macaulay filtered D-module is filtered perverse.