Microlocal Riemann–Hilbert Correspondence

Abstract

We construct the global microlocal Riemann–Hilbert correspondence as an explicit equivalence between the abelian stack of microlocal perverse sheaves defined in [W] and the abelian stack of regular holonomic microdifferential modules of [KK]. The theory of analytic ind-sheaves and its microlocalization is crucial for our construction since it allows us to define solution complexes with values in the (ind-)ring of microlocal holomorphic functions (resp. microlocal tempered holomorphic functions).