Skeletons and moduli of Stokes torsors

TL;DR

This paper proves a skeleton conjecture analogue for Stokes torsors, establishing a finite type affine scheme representation and deriving finiteness results for multivariable differential systems.

Contribution

It introduces a new skeleton conjecture analogue for Stokes torsors and demonstrates the representability of their moduli space as an affine scheme of finite type.

Findings

Proves an analogue of Deligne's skeleton conjecture for Stokes torsors.

Establishes the representability of the functor of relative Stokes torsors by an affine scheme.

Derives strong finiteness results for integrable systems in several variables.

Abstract

We prove an analogue for Stokes torsors of Deligne's skeleton conjecture and deduce from it the representability of the functor of relative Stokes torsors by an affine scheme of finite type over C. This provides, in characteristic 0, a local analogue of the existence of a coarse moduli for skeletons with bounded ramification, due to Deligne. As an application, we use the geometry of this moduli to derive quite strong finiteness results for integrable systems of differential equations in several variables which did not have any analogue in one variable.