Microlocal perverse sheaves

TL;DR

This paper constructs the stack of microlocal perverse sheaves on complex manifolds using complexes of analytic ind-sheaves, enabling a microlocal Riemann-Hilbert correspondence with regular holonomic microdifferential modules.

Contribution

It provides an explicit construction of microlocal perverse sheaves as complexes of analytic ind-sheaves and establishes their equivalence with regular holonomic microdifferential modules.

Findings

Explicit construction of microlocal perverse sheaves as complexes of ind-sheaves

Formulation of the microlocal Riemann-Hilbert correspondence

Equivalence of stacks with regular holonomic microdifferential modules

Abstract

We give an explicit construction of the stack of microlocal perverse sheaves on the projective cotangent bundle of a complex manifold. Microlocal perverse sheaves will be represented as complexes of analytic ind-sheaves which have recently been studied by Kashiwara-Schapira. This description allows us to formulate the microlocal Riemann-Hilbert correspondance in order to establish an equivalence of stacks with the stack of regular holonomic microdifferential modules.