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Mochizuki, Takuro.

Mixed Twistor D-modules [electronic resource] / by Takuro Mochizuki. - 1st ed. 2015. - XX, 487 p. online resource. - Lecture Notes in Mathematics, 2125 0075-8434 ; . - Lecture Notes in Mathematics, 2125 .

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.

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. .

ISBN: 9783319100883

Standard No.: 10.1007/978-3-319-10088-3 doi

Subjects--Topical Terms:
Functions of complex variables.
Algebraic geometry.
Several Complex Variables and Analytic Spaces.
Algebraic Geometry.

LC Class. No.: QA331.7

Dewey Class. No.: 515.94