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On a topological counterpart of regularization for holonomic $$\mathscr{D}$$-modules. (Sur un analogue topologique de la régularisation pour les $$\mathscr{D}$$-modules holonomes.) (English. French summary) Zbl 07282221
Summary: On a complex manifold, the embedding of the category of regular holonomic $$\mathscr{D}$$-modules into that of holonomic $$\mathscr{D}$$-modules has a left quasi-inverse functor $$\mathscr{M}\rightarrow\mathscr{M}_{\text{reg}}$$, called regularization. Recall that $$\mathscr{M}_{\text{reg}}$$ is reconstructed from the de Rham complex of $$\mathscr{M}$$ 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.
##### MSC:
 32C38 Sheaves of differential operators and their modules, $$D$$-modules 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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##### References:
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