Mixed Twistor D-modules

1. Auflage 2015
ISBN: 978-3-319-10087-6
Verlag: Springer International Publishing

Buch, Englisch, Band 2125, 487 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 7664 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Mochizuki, Takuro

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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.