A microlocal version of the Riemann-Hilbert correspondence
type: Item
instance of: scholarly article
title: A microlocal version of the Riemann-Hilbert correspondence
zbMATH Open document ID: 0839.32004
DOI: 10.12775/TMNA.1994.036
author: Emmanuel Andronikof
published in: Topological Methods in Nonlinear Analysis
publication date: 1996-06-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 18F20
zbMATH DE Number: 828291
zbMATH Keywords: holonomic systems
zbMATH Keywords: perverse sheaves
zbMATH Keywords: Riemann-Hilbert correspondence
reviewed by: Masakazu Muro
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 828291