Stokes structure of mild difference modules

TL;DR

This paper develops a new categorical framework for understanding the Stokes phenomenon in linear difference equations with mild singularities, extending classical Riemann-Hilbert correspondence concepts.

Contribution

It introduces a category of filtered sheaves on a circle to describe the Stokes phenomenon and establishes a mild difference analog of the Riemann-Hilbert correspondence.

Findings

Established a categorical description of the Stokes phenomenon for difference equations.

Proved an analog of the Riemann-Hilbert correspondence for germs of meromorphic connections.

Extended classical theory to the setting of difference modules with mild singularities.

Abstract

We introduce a category of filtered sheaves on a circle to describe the Stokes phenomenon of linear difference equations with mild singularity. The main result is a mild difference analog of the Riemann-Hilbert correspondence for germs of meromorphic connections in one complex variable by Deligne-Malgrange.