Sur une variété complexe lisse, l’inclusion de la catégorie des -modules holonomes réguliers dans celle des -modules holonomes admet un foncteur quasi-inverse à gauche , appelé régularisation. Rappelons que est reconstruit à partir du complexe de de Rham de par la correspondance de Riemann-Hilbert régulière. De même, sur un espace topologique, l’inclusion des faisceaux dans les ind-faisceaux enrichis admet un foncteur quasi-inverse à gauche, qu’on appelle ici faisceautisation. La régularisation et la faisceautisation sont échangées par la correspondance de Riemann-Hilbert irrégulière. Dans ce travail, nous étudions certaines des propriétés du foncteur de faisceautisation. En particulier, nous fournissons une formule qui calcule la fibre du faisceautisé de la spécialisation et de la microlocalisation enrichies.
On a complex manifold, the embedding of the category of regular holonomic -modules into that of holonomic -modules has a left quasi-inverse functor , called regularization. Recall that is reconstructed from the de Rham complex of by the regular Riemann-Hilbert correspondence. Similarly, on a topological space, the embedding of sheaves into enhanced ind-sheaves has a left quasi-inverse functor, called here sheafification. Regularization and sheafification are intertwined by the irregular Riemann-Hilbert correspondence. Here, we study some of the properties of the sheafification functor. In particular, we provide a stalk formula for the sheafification of enhanced specialization and microlocalization.
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@article{JEP_2021__8__27_0,
author = {Andrea D{\textquoteright}Agnolo and Masaki Kashiwara},
title = {On a topological counterpart of regularization for holonomic $\protect \mathscr{D}$-modules},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {27--55},
publisher = {\'Ecole polytechnique},
volume = {8},
year = {2021},
doi = {10.5802/jep.140},
zbl = {07282221},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.140/}
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JO - Journal de l’École polytechnique — Mathématiques
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Andrea D’Agnolo; Masaki Kashiwara. On a topological counterpart of regularization for holonomic $\protect \mathscr{D}$-modules. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 27-55. doi : 10.5802/jep.140. https://jep.centre-mersenne.org/articles/10.5802/jep.140/
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