A \v{C}ech--Stokes Pushout Groupoid: a Log/Kummer Betti Presenter for Stokes Torsors

TL;DR

This paper provides an explicit Betti presentation of Stokes torsors for meromorphic flat connections with prescribed irregular types, using a boundary Cech--Stokes groupoid and explicit pushout constructions.

Contribution

It introduces a strictly 1-categorical, cover-based Betti presentation for Stokes torsors, incorporating a boundary model and explicit gluing methods.

Findings

Constructed a boundary Cech--Stokes groupoid for Stokes torsors.

Proved the boundary Stokes moduli are sections of a natural forgetful functor.

Derived a canonical groupoid presentation computing global Stokes objects.

Abstract

We give an explicit Betti presentation of the Stokes torsors attached to meromorphic flat connections of prescribed irregular type along a simple normal crossings divisor, at fixed Kummer level. Our construction is strictly 1-categorical and cover-based: on a punctured logarithmic collar of the divisor, we define a small Cech--Stokes groupoid and prove that the boundary Stokes moduli is described by sections of a natural forgetful functor, rather than by representations of the decorated boundary groupoid itself. By gluing this boundary model to the ordinary Cech presenter of the complement through an explicit pushout construction, we obtain a groupoid presentation that computes the global Stokes objects. The resulting presentation is canonical up to Morita equivalence, compatible with Kummer descent along all normal crossings strata, and admits an explicit finite local description near corners in terms of nonabelian cocycles and relations.