A microlocal version of the Riemann-Hilbert correspondence (Q1904455)

Let \(X\) be a complex manifold. We denote by \textit{Reghol}\(({\mathcal D}_X)\) the category of regular holonomic systems on \(X\) and by \textit{Perv}\((X)^0\) that of perverse sheaves on \(X\). There exists a category equivalence between them, which is called Riemann-Hilbert correspondence. The purpose of this paper is to build a microlocal version of the correspondence. The authors construct the microlocalization of \textit{Perv}\((X)^0\) and \textit{Reghold}\(({\mathcal D}_X)\) at a point \(p \in T*X - X\). They are category equivalent to each other.