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.
CITATION STYLE
Mochizuki, T. (2015). Mixed Twistor D-modules. Mixed Twistor D-modules (Vol. 2125, pp. 1–487). Springer International Publishing. https://doi.org/10.1007/978-3-319-10088-3
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