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Moduli of pre-$$\mathcal D$$-modules, perverse sheaves and the Riemann-Hilbert morphism. I. (English) Zbl 0853.14004
We construct a moduli scheme for semistable pre-$${\mathcal D}$$-modules with prescribed singularities and numerical data on a smooth projective variety. These pre-$${\mathcal D}$$-modules are to be viewed as regular holonomic $${\mathcal D}$$-modules with ‘level structure’. We also construct a moduli scheme for perverse sheaves on the variety with prescribed singularities and other numerical data, and represent the de Rham functor (which gives the Riemann-Hilbert correspondence) by an analytic morphism between the two moduli schemes.
Reviewer: N.Nitsure (Bombay)

##### MSC:
 14D20 Algebraic moduli problems, moduli of vector bundles 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 32G81 Applications of deformations of analytic structures to the sciences 32C38 Sheaves of differential operators and their modules, $$D$$-modules
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