Mixed Twistor D-modules

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...