On a topological counterpart of regularization for holonomic D-modules

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 $\mathcal{M}\mapsto {\mathcal{M}}_{\mathrm{reg}}$, called regularization. Recall that ${\mathcal{M}}_{\mathrm{reg}}$ is reconstructed from the de Rham complex of $\mathcal{M}$ 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 their properties. In particular, we provide a germ formula for the sheafification of enhanced specialization and microlocalization.

arXiv comment31 pages

References in corpus (6)

• Riemann-Hilbert correspondence for holonomic D-modules
• Microlocal study of ind-sheaves I: micro-support and regularity
• Enhanced perversities
• A microlocal approach to the enhanced Fourier-Sato transform in dimension one
• Riemann-Hilbert correspondence for irregular holonomic D-modules
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Cited by in corpus (1)

• Enhanced nearby and vanishing cycles in dimension one and Fourier transform