A description of monodromic mixed Hodge modules
| Autor: | Saito, Takahiro |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a smooth algebraic variety $X$, a monodromic $D$-module on $X\times \mathbb{C}$ is decomposed into a direct sum of some $D$-modules on $X$. We show that the Hodge filtration of a mixed Hodge module on $X\times \mathbb{C}$ 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 $X\times \mathbb{C}$ 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. Comment: 46 pages, to appear in Journal f\"ur die reine und angewandte Mathematik |
| Databáze: | arXiv |
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