JournalsprimsVol. 41 , No. 1DOI 10.2977/prims/1145475404

Microlocal Riemann–Hilbert Correspondence

  • Ingo Waschkies

    Université Pierre et Marie Curie, Paris, France
Microlocal Riemann–Hilbert Correspondence cover

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).