Classification de modules aux diff\'erences filtr\'es isogradu\'es

TL;DR

This paper establishes the existence of a moduli scheme, specifically an affine space, for classifying filtered q-difference modules with a fixed associated graded module, advancing the understanding of irregular q-difference equations.

Contribution

It generalizes the classification problem by proving the existence of an affine moduli scheme for filtered q-difference modules with prescribed graded modules.

Findings

Existence of a moduli scheme as an affine space.

Applicable to local analytic classification of irregular q-difference equations.

Provides a framework for classifying filtered modules with fixed graded structure.

Abstract

The local analytic classification of irregular linear q-difference equations (Ramis-Sauloy-Zhang) involves the classfication of filtered q-difference modules with a prescribed associated graded module. We prove in a more general setting the existence for this problem of a moduli scheme which is an affine space. ----- La classification analytique locale des equations aux q-differences irregulieres se ramene a la classification de modules aux q-differences filtres a gradue fixe. Nous degageons ici des hypotheses generales qui assurent l'existence d'un schema de modules pour ce probleme, qui soit de plus un espace affine.