Introduction to Stokes structures

TL;DR

This paper introduces Stokes-perverse sheaves as a framework for the Riemann-Hilbert correspondence in holonomic D-modules, extending Deligne's ideas to higher dimensions with recent advances by Mochizuki.

Contribution

It develops the concept of Stokes-perverse sheaves, generalizes Deligne's dimension one approach, and initiates a higher-dimensional framework for the Riemann-Hilbert correspondence.

Findings

Explicit cases of the Riemann-Hilbert correspondence are made clear.

The notion of Stokes-perverse sheaves is formalized for higher dimensions.

Connections to recent results of T. Mochizuki are established.

Abstract

The purpose of these lectures is to introduce the notion of a Stokes-perverse sheaf as a receptacle for the Riemann-Hilbert correspondence for holonomic D-modules. They develop the original idea of P. Deligne in dimension one, and make it enter the frame of perverse sheaves. They also give a first step for a general definition in higher dimension, and make explicit particular cases of the Riemann-Hilbert correspondence, relying on recent results of T. Mochizuki.