On the de Rham Complex of Mixed Twistor 𝒟-Modules

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 $\mathscr O_s$-modules on X×S. We prove that the de Rham complex of a holonomic $\mathscr D_{X\times S/S}$-module which is $\mathscr O_s$-flat as well as its dual object is perverse relatively to this t-structure. This result applies to mixed twistor $\mathscr D$-modules.