FILTERED PERVERSE COMPLEXES

We introduce the notion of filtered perversity of a filtered different ial complex on a complex analytic manifold X, without any assumptions of coherence, with the purpose of studying the connection between the pure Hedge modules and the L-2-complexes. We show that if a filtered d ifferential complex (M-.,F-.) is filtered perverse then DR-1(M-., F.) is isomorphic to a filtered D-module; a coherence assumption on the co homology of (M,F) implies that, in addition, this D-module is holonomi c. We show the converse: the de Rham complex of a holonomic Cohen-Maca ulay filtered D-module is filtered perverse.