Mixed Hodge Modules

Abstract

The definition of mixed Hodge modules is very involved. For this reason it is more suitable to start with an axiomatic introduction. This makes it possible to deduce important results rather painlessly, such as the existence of pure Hodge structures on the intersection cohomology groups. Hodge modules are generalizations of variations of Hodge structures. In fact, a variation of Hodge structures is a basic example of a Hodge module. In the world of Hodge modules the underlying (complexified) local system with its integrable connection and filtration is to be considered as a filtered D-module. The local system itself must be replaced by its perverse intersection complex.