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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.
32C38 Sheaves of differential operators and their modules, \(D\)-modules
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
Full Text: DOI
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