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A local Galois \(D\)-groupoid for Fuchsian \(q\)-difference systems. (Un \(D\)-groupoïde de Galois local pour les systèmes aux \(q\)-différences fuchsiens.) (French) Zbl 1186.39007

Summary: We compute the Galois \(D\)-groupoid of a constant linear \(q\)-difference system and we define, giving its realisations, a local Galois \(D\)-groupoid for Fuchsian \(q\)-difference systems.

MSC:

39A13 Difference equations, scaling (\(q\)-differences)
20N02 Sets with a single binary operation (groupoids)
12H05 Differential algebra
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References:

[1] Malgrange, B., Le groupoïde de Galois d’un feuilletage, Monographie de l’Enseignement Mathématique, 38, 2, 465-501 (2001) · Zbl 1033.32020
[2] Sauloy, J., Galois theory of Fuchsian \(q\)-difference equations, Annales Scientifiques de l’École Normale Supérieure Quatrième Série, 36, 925-968 (2003) · Zbl 1053.39033
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