Filtered perverse complexes

We introduce the notion of {\em 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 {$L^2$}-complexes. We show that if a filtered differential complex $({\cal {M}}^\bullet,F_\bullet)$ is filtered perverse then $\aDR({\cal {M}}^\bullet,F_\bullet)$ is isomorphic to a filtered $\cal{D}$-module; a coherence assumption on the cohomology of $({\cal {M}}^\bullet,F_\bullet)$ implies that, in addition, this $\cal {D}$-module is holonomic. We show the converse: the de Rham complex of a holonomic Cohen-Macaulay filtered $\cal {D}$-module is filtered perverse.

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Published 1 January 1998