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RIEMANN–HILBERT CORRESPONDENCE FOR MIXED TWISTOR
${\mathcal{D}}$-MODULES
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 18 / Issue 3 / May 2019
- Published online by Cambridge University Press:
- 19 May 2017, pp. 629-672
- Print publication:
- May 2019
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- Article
- Export citation
-
We introduce the notion of regularity for a relative holonomic
${\mathcal{D}}$-module in the sense of Monteiro Fernandes and Sabbah [Internat. Math. Res. Not. (21) (2013), 4961–4984]. 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.
