A description of monodromic mixed Hodge modules

For a smooth algebraic variety X, a monodromic D-module on X x C is decomposed into a direct sum of some D-modules on X. We show that the Hodge filtration of a mixed IIodge module on X x C whose underlying D-module is monodromic is also decomposed. Moreover, we show that there is an equivalence of categories between the category of monodromic mixed Hodge modules on X x C and the category of gluing data. As an application, we endow the Fourier-Laplace transformation of the underlying D-module of a monodromic mixed Hodge module with a mixed Hodge module structure.

Automated summary

In this paper, we study the decomposition of monodromic D-modules and mixed Hodge modules on a smooth algebraic variety, as well as the equivalence between the category of monodromic mixed Hodge modules and the category of gluing data. We also provide a mixed Hodge module structure for the Fourier-Laplace transformation of the underlying D-module of a monodromic mixed Hodge module.