Mixed twistor D-modules

Original · EN

We introduce mixed twistor D-modules, and establish the fundamental functorial property. We also prove that they are described as the gluing of admissible variations of mixed twistor structure. In a sense, mixed twistor D-modules could be regarded as a twistor version of mixed Hodge modules due to M. Saito. In the other sense, they could be a mixed version of pure twistor D-modules studied by C. Sabbah and the author. A theory of mixed twistor D-modules is one of the ultimate goals in the study suggested by Simpson's Meta Theorem, and the author hopes that it would play a basic role in the Hodge theory for holonomic D-modules possibly with irregular singularity.