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).
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Ingo Waschkies, Microlocal Riemann–Hilbert Correspondence. Publ. Res. Inst. Math. Sci. 41 (2005), no. 1, pp. 37–72DOI 10.2977/PRIMS/1145475404