Mochizuki T. Mixed Twistor D-modules

Springer International Publishing, 2015. — 487 p. — (Lecture Notes in Mathematics 2125). — ISBN: 978-3-319-10088-3; 978-3-319-10087-6.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.Preliminary
Canonical Prolongations
Gluing and Specialization of R-Triples
Gluing of Good-KMS Smooth R-Triples
Preliminary for Relative Monodromy Filtrations
Mixed Twistor D-Modules
Infinitesimal Mixed Twistor Modules
Admissible Mixed Twistor Structures and Their Variants
Good Mixed Twistor D-Modules
Some Basic Property
D-Triples and Their Functoriality
Duality and Real Structure of Mixed Twistor D-Modules
Algebraic Mixed Twistor D-Modules and Their Derived Category
Good Systems of Ramified Irregular Values