Riemann-Hilbert correspondence for mixed twistor D-Modules

Abstract

We introduce the notion of regularity for a relative holonomic $\mathcal{D}$-module in the sense of arXiv:1204.1331. We prove that the solution functor from the bounded derived category of regular relative holonomic modules to that of relative constructible complexes is essentially surjective by constructing a right quasi-inverse functor. When restricted to relative $\mathcal{D}$-modules underlying a regular mixed twistor $\mathcal{D}$-module, this functor satisfies the left quasi-inverse property.

36 pages. V2: 40 pages, statement of Theorem 5 corrected, a correction in the proof of Lemma 3.15, presentation improved with more introductory material

References in corpus (2)

• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules
• On the de Rham complex of mixed twistor D-modules

Cited by in corpus (4)

• Relative regular Riemann-Hilbert correspondence
• Relative Regular Riemann-Hilbert correspondence II
• The relative hermitian duality functor
• Relative strongly regular holonomic $\mathcal{D}$-modules and the Riemann-Hilbert correspondence