Algebraic construction of the Stokes sheaf for irregular linear q-difference equations

Abstract

The local analytic classification of irregular linear q-difference equations has recently been obtained by J.-P. Ramis, J. Sauloy and C. Zhang. Their description involves a q-analog of the Stokes sheaf and theorems of Malgrange-Sibuya type and is based on a discrete summation process due to C. Zhang. We show here another road to some of these results by algebraic means and we describe the q-Gevrey devissage of the q-Stokes sheaf by holomorphic vector bundles over an elliptic curve.

References in corpus (1)

• La filtration canonique par les pentes d'un module aux q-différences et le gradué associé

Cited by in corpus (8)

• Building meromorphic solutions of $q$-difference equations using a Borel-Laplace summation
• The q-analogue of the wild fundamental group (II)
• Intrinsic approach to Galois theory of q-difference equations, with the preface to Part 4 "The Galois D-groupoid of a q-difference system'' by Anne Granier
• q-Deformation of Meromorphic Solutions of Linear Differential Equations
• Asymptotic formulae of two divergent bilateral basic hypergeometric series
• Symmetries in Connection Preserving Deformations
• On local solutions of the Ramanujan equation and their connection formulae
• The Stokes phenomenon for the Ramanujan's $q$-difference equation and its higher order extension