an:07282221
Zbl 07282221
D'Agnolo, Andrea; Kashiwara, Masaki
On a topological counterpart of regularization for holonomic \(\mathscr{D}\)-modules
EN
J. ??c. Polytech., Math. 8, 27-55 (2021).
00455861
2021
j
32C38 14F10
irregular Riemann-Hilbert correspondence; enhanced perverse sheaves; holonomic \(\mathscr{D}\)-modules
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.