2020/12/29 by Takahiro Saito, Saito, Takahiro
Mathematics · #14F10 #32S35 #32S40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2012.14671
openalex publication_date 2020/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a smooth algebraic variety X, a monodromic D-module on X× 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 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 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.