The derived Riemann-Hilbert correspondence

Abstract: In this short paper we prove a derived version of the Riemann-Hilbert correspondence of Deligne and Simpson. Our generalization is twofold: on one side we consider families of representations of the full homotopy type of a smooth analytic space $X$ in the stable $\infty$-category of complexes of coherent sheaves and of perfect complexes; on the other side, we allow the base parametrizing such families to be derived $\mathbb C$-analytic spaces.