no. 4
The Hodge filtration of a monodromic mixed Hodge module and the irregular Hodge filtration
[La filtration de Hodge d’un module de Hodge mixte monodromique et la filtration de Hodge irrégulière]
Saito, Takahiro1
1 Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502 (Japan)
Annales de l'Institut Fourier, Tome 74 (2024) no. 4, pp. 1603-1670.

Pour un fibré vectoriel algébrique E sur une variété algébrique lisse X, un D-module monodromique sur E est décomposé en une somme directe de certains O-modules sur X. Nous montrons que la filtration de Hodge d’un module de Hodge mixte monodromique est décomposée par rapport à la décomposition du D-module sous-jacent. En utilisant ce résultat, nous munissons la transformée de Fourier–Laplace M ∧ du D-module sous-jacent M à un module de Hodge mixte monodromique d’une structure de module de Hodge mixte. De plus, nous décrivons explicitement la filtration de Hodge irrégulière sur M ∧ et montrons qu’elle coïncide avec la filtration de Hodge aux indices entiers.

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 ∧ 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 ∧ concretely and show that it coincides with the Hodge filtration at all integer indices.

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Révisé le :
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DOI : 10.5802/aif.3629
Classification : 14F10, 32S35, 32S40
Keywords: $D$-module, Perverse sheaf, Mixed Hodge module, Mixed twistor $D$-module, Irregular Hodge filtration.
Mots-clés : $D$-module, faisceau pervers, module de Hodge mixte, $D$-module de twisteur mixte, filtration de Hodge irrégulière.

Saito, Takahiro 1

1 Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502 (Japan)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Saito, Takahiro. The Hodge filtration of a monodromic mixed Hodge module and the irregular Hodge filtration. Annales de l'Institut Fourier, Tome 74 (2024) no. 4, pp. 1603-1670. doi : 10.5802/aif.3629. https://aif.centre-mersenne.org/articles/10.5802/aif.3629/

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