We introduce mixed twistor D-modules and establish their fundamental functorial properties. We also prove that they can be described as the gluing of admissible variations of mixed twistor structures. In a sense, mixed twistor D-modules can be regarded as a twistor version of M. Saito's mixed Hodge modules. Alternatively, they can be viewed as a mixed version of the pure twistor D-modules studied by C. Sabbah and the author. The theory of mixed twistor D-modules is one of the ultimate goals in the study suggested by Simpson's Meta Theorem and it would form a foundation for the Hodge theory of holonomic D-modules which are not necessarily regular singular.

The first book on mixed twistor D-modules Forms a tentative foundation of generalized Hodge theory of holonomic D-modules Represents one of the final goals in the study of mixed twistor structures Includes supplementary material: sn.pub/extras

Autorentext

Takuro Mochizuki has been awarded the 2022 Breakthrough Prize in Mathematics for advancing the understanding of holonomic D-modules through his research on harmonic bundles and twister D-modules, which he has studied at the "interface of algebraic geometry and differential geometry".

Inhalt
Introduction.- Preliminary.- Canonical prolongations.- Gluing and specialization of r-triples.- Gluing of good-KMS r-triples.- Preliminary for relative monodromy filtrations.- Mixed twistor D-modules.- Infinitesimal mixed twistor modules.- Admissible mixed twistor structure and variants.- Good mixed twistor D-modules.- Some basic property.- Dual and real structure of mixed twistor D-modules.- Derived category of algebraic mixed twistor D-modules.- Good systems of ramified irregular values.