Regular and irregular holonomic D-modules

TL;DR

This survey explores the theory of regular and irregular holonomic D-modules, emphasizing their solutions, the Riemann-Hilbert correspondence, and recent advances in the irregular case using indsheaves.

Contribution

It provides a comprehensive overview of the main results and recent developments in the theory of holonomic D-modules, including irregular cases, based on lectures at IHES.

Findings

Main results on tempered holomorphic solutions of D-modules

Riemann-Hilbert correspondence for regular holonomic modules

Enhanced theory for irregular holonomic D-modules

Abstract

This is a survey paper based on a series of lectures given at the IHES in February/March 2015. In a first part, we recall the main results on the tempered holomorphic solutions of D-modules in the language of indsheaves and, as an application, the Riemann-Hilbert correspondence for regular holonomic modules. In a second part, we present the enhanced version of the first part, treating along the same lines the irregular holonomic case.