A description of monodromic mixed Hodge modules

Abstract

Abstract For a smooth algebraic variety X, a monodromic D-module on X × ℂ {X\times\mathbb{C}} is decomposed into a direct sum of some D-modules on X. We show that the Hodge filtration of a mixed Hodge module on X × ℂ {X\times\mathbb{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 × ℂ {X\times\mathbb{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.