Abstract:
The classical theorem of Corlette says that there is a correspondence between semisimple flat bundles and harmonic bundles on a smooth projective variety. Rather recently, it has been generalized to
the correspondence between polarizable pure twistor D-modules and semisimple holonomic D-modules.
It enables us to use techniques in global analysis for the study on D-modules. As a remarkable application,
as conjectured by Kashiwara, we obtain that a projective push-forward preserves semisimplicity of holonomic D-modules, and that a decomposition theorem holds for semisimple holonomic D-modules.
The plan of my lecture is as follows:
- 1. Introduction of harmonic bundle
- 2. Asymptotic behaviour around singularity
- 3. Kobayashi-Hitchin correspondence
- 4. Good formal structure and Stokes structure of meromorphic flat bundles
- 5. Twistor structure and Simpson's meta-theorem
- 6. Introduction to polarizable pure twistor D-module
Series of lectures
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