Stokes filtered sheaves and differential-difference modules

TL;DR

This paper introduces Stokes filtered quasi-local systems, proving their category is abelian and providing a geometric construction method to analyze the asymptotic behavior of solutions to differential-difference modules.

Contribution

It defines Stokes filtered quasi-local systems, proves their categorical properties, and offers a geometric construction approach for studying differential-difference modules.

Findings

Category of Stokes filtered quasi-local systems is abelian

Provides a geometric construction method

Describes asymptotic behavior of solutions

Abstract

We introduce the notion of Stokes filtered quasi-local systems. It is proved that the category of Stokes filtered quasi-local systems is abelian. We also give a geometric way to construct Stokes filtered quasi-local systems, which describe the asymptotic behavior of certain classes of solutions to some differential-difference modules.