Filtered Perverse Complexes

Details Filtered Perverse Complexes Filtered Perverse Complexes

1996-07-19

arxiv.org/abs/alg-geom/9607020v4

Mathematics

Algebraic Geometry

AMSLaTeX v 1.1. This version is a major revision. With the new co-author (M.Saito) it contains substantially new results, impr

Scientific paper

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 \lt-complexes. We show that if a filtered differential complex $(\cM^\bullet,F_\bullet)$ is filtered perverse then $\aDR(\cM^\bullet,F_\bullet)$ is isomorphic to a filtered $\cD$-module; a coherence assumption on the cohomology of $(\cM^\bullet,F_\bullet)$ implies that, in addition, this $\cD$-module is holonomic. We show the converse: the de Rham complex of a holonomic Cohen-Macaulay filtered $\cD$-module is filtered perverse.

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