On Some Topological Properties of Fourier Transforms of Regular Holonomic D-Modules

TL;DR

This paper investigates the topological properties of Fourier transforms of regular holonomic D-modules, demonstrating their solution complexes are monodromic and providing new insights and proofs related to classical theorems in the field.

Contribution

It introduces new topological results about Fourier transforms of regular holonomic D-modules and offers an improved proof and a converse to Brylinski's classical theorem.

Findings

Solution complexes are monodromic

Application to irregular holonomic D-modules

Enhanced proof and converse of Brylinski's theorem

Abstract

We study Fourier transforms of regular holonomic D-modules. In particular we show that their solution complexes are monodromic. An application to direct images of some irregular holonomic D-modules will be given. Moreover we give a new proof to the classical theorem of Brylinski and improve it by showing its converse.