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This article constructs Von Neumann invariants for constructible complexesand coherent D-modules on compact complex manifolds, generalizing the work ofthe author on coherent L 2-cohomology. We formulate a conjecturalgeneralization of Dingoyan's L 2-Mixed Hodge structures in terms of Saito'sMixed Hodge Modules and give partial results in this direction. 2020 AMSClassification: 32J27.

Towards a L 2 cohomology theory for Hodge modules on infinite covering  spaces: L 2 constructible cohomology and L 2 de Rham cohomology for coherent  D-modules