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On the de Rham complex of mixed twistor \(\mathcal{D}\)-modules. (English) Zbl 1312.14059

Summary: Given a complex manifold \(S\), we introduce for each complex manifold \(X\) a \(t\)-structure on the bounded derived category of \(\mathbb{C}\)-constructible complexes of \(\mathcal O_S\)-modules on \(X\times S\). We prove that the de Rham complex of a holonomic \(\mathcal D_{X\times S/S}\)-module which is \(\mathcal O_S\)-flat as well as its dual object is perverse relatively to this \(t\)-structure. This result applies to mixed twistor \(\mathcal D\)-modules.

MSC:

14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
32C38 Sheaves of differential operators and their modules, \(D\)-modules
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