Mixed twistor D-modules

Abstract

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.

Cited by in corpus (11)

• On the irregular Hodge filtration of exponentially twisted mixed Hodge modules
• Twistor property of GKZ-hypergeometric systems
• Algebraic aspects of hypergeometric differential equations
• Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
• Riemann-Hilbert correspondence for mixed twistor D-Modules
• Relative regular Riemann-Hilbert correspondence
• Hypergeometric Hodge modules
• A twistor approach to the Kontsevich complexes
• Logarithmic Comparison with smooth boundary divisor in Mixed Hodge Modules
• Rescalability of integrable mixed twistor $D$-modules
• The Künneth Formula for the Twisted de Rham and Higgs Cohomologies