L 2 -Constructible Cohomology and L 2 -De Rham Cohomology for coherent 𝒟-modules

This article constructs Von Neumann invariants for constructible complexes and coherent 𝒟-modules on compact complex manifolds, generalizing the work of the author on coherent L 2 -cohomology. We formulate a conjectural generalization of Dingoyan’s L 2 - Mixed Hodge structures in terms of Saito’s Mixed Hodge Modules and give partial results in this direction.