2022/04/28 by Takahiro Saito, Saito, Takahiro
Mathematics · #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.2204.13381
openalex publication_date 2022/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an algebraic vector bundle E over a smooth algebraic variety X, a monodromic D-module on E is decomposed into a direct sum of some O-modules on X. We show that the Hodge filtration of a monodromic mixed Hodge module is decomposed with respect to the decomposition of the underlying D-module. By using this result, we endow the Fourier-Laplace transform M\wedge of the underlying D-module M of a monodromic mixed Hodge module with a mixed Hodge module structure. Moreover, we describe the irregular Hodge filtration on M\wedge concretely and show that it coincides with the Hodge filtration at all integer indices.