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

2022/03/14 by Eyssidieux, Philippe · 1 citation
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.06950

Abstract

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. 2020 AMS Classification: 32J27.

Cited by

• Structure theorems for the heart of LCA

Related

• L² Cohomology on coverings of a compact Kähler manifold
• Invariants de Von Neumann des faisceaux coherents
• Mixed Hodge Structures
• L²-representation of Hodge Modules
• Hodge theory and A_∞ structures on cohomology