[Sur un analogue topologique de la régularisation pour les -modules holonomes]
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.
Accepté le :
Publié le :
DOI : 10.5802/jep.140
Keywords: Irregular Riemann-Hilbert correspondence, enhanced perverse sheaves, holonomic D-modules
Mot clés : Correspondance de Riemann-Hilbert irrégulière, faisceau pervers enrichi, D-module holonome
@article{JEP_2021__8__27_0,
author = {D{\textquoteright}Agnolo, Andrea and Kashiwara, Masaki},
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 = {http://www.numdam.org/articles/10.5802/jep.140/}
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TY - JOUR
AU - D’Agnolo, Andrea
AU - Kashiwara, Masaki
TI - On a topological counterpart of regularization for holonomic $\protect \mathscr{D}$-modules
JO - Journal de l’École polytechnique — Mathématiques
PY - 2021
SP - 27
EP - 55
VL - 8
PB - Ecole polytechnique
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DO - 10.5802/jep.140
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D’Agnolo, Andrea; Kashiwara, Masaki. 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. http://www.numdam.org/articles/10.5802/jep.140/
[1] Riemann-Hilbert correspondence for holonomic D-modules, Publ. Math. Inst. Hautes Études Sci., Volume 123 (2016), pp. 69-197 | DOI | MR | Zbl
[2] A microlocal approach to the enhanced Fourier-Sato transform in dimension one, Adv. Math., Volume 339 (2018), pp. 1-59 | DOI | MR | Zbl
[3] Enhanced perversities, J. reine angew. Math., Volume 751 (2019), pp. 185-241 | DOI | MR | Zbl
[4] Enhanced specialization and microlocalization, 2019 | arXiv
[5] Microlocal theory of sheaves and Tamarkin’s non displaceability theorem, Homological mirror symmetry and tropical geometry (Lect. Notes Unione Mat. Ital.), Volume 15, Springer, Cham, 2014, pp. 43-85 | DOI | MR | Zbl
[6] On irregularities of Fourier transforms of regular holonomic -modules, Adv. Math., Volume 366 (2020), p. 107093, 62 | DOI | MR | Zbl
[7] The Riemann-Hilbert problem for holonomic systems, Publ. RIMS, Kyoto Univ., Volume 20 (1984) no. 2, pp. 319-365 | DOI | MR | Zbl
[8] Riemann-Hilbert correspondence for irregular holonomic -modules, Japan. J. Math., Volume 11 (2016) no. 1, pp. 113-149 | DOI | MR | Zbl
[9] Sheaves on manifolds, Grundlehren Math. Wiss., 292, Springer-Verlag, Berlin, Heidelberg, 1990 | MR | Zbl
[10] Ind-sheaves, Astérisque, 271, Société Mathématique de France, Paris, 2001 | Numdam | Zbl
[11] Microlocal study of ind-sheaves. I. Micro-support and regularity, Autour de l’analyse microlocale (Astérisque), Volume 284, Société Mathématique de France, Paris, 2003, pp. 143-164 | Numdam | Zbl
[12] Regular and irregular holonomic D-modules, London Math. Soc. Lect. Note Series, 433, Cambridge University Press, Cambridge, 2016 | DOI | MR | Zbl
[13] Microlocal condition for non-displaceability, Algebraic and analytic microlocal analysis (Springer Proc. Math. Stat.), Volume 269, Springer, Cham, 2018, pp. 99-223 | DOI | MR | Zbl
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