On a complex manifold, the embedding of the category of regular holonomic D-modules into that of holonomic D-modules has a left quasi-inverse functor $mathcalMmapstomathcalM_mathrmreg$, called regularization. Recall that $mathcalM_mathrmreg$ is reconstructed from the de Rham complex of $mathcalM$ 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 their properties. In particular, we provide a germ formula for the sheafification of enhanced specialization and microlocalization.

On a topological counterpart of regularization for holonomic D-modules

Andrea D'Agnolo;
2021

Abstract

On a complex manifold, the embedding of the category of regular holonomic D-modules into that of holonomic D-modules has a left quasi-inverse functor $mathcalMmapstomathcalM_mathrmreg$, called regularization. Recall that $mathcalM_mathrmreg$ is reconstructed from the de Rham complex of $mathcalM$ 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 their properties. In particular, we provide a germ formula for the sheafification of enhanced specialization and microlocalization.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3326471
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