The canonical filtration by the slopes of a \(q\)-difference module and the associated graded module.

DOI10.5802/aif.2015zbMath1061.39013arXivmath/0210430OpenAlexW125095063MaRDI QIDQ1890152

Jacques Sauloy

Publication date: 20 December 2004

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210430

zbMATH Keywords

asymptotic behaviorNewton polygon\(q\)-difference equations\(q\)-difference operatorcanonical filtration\(q\)-difference modulefiltration by the slopes

Mathematics Subject Classification ID

Difference equations, scaling ((q)-differences) (39A13)

Related Items (16)

On classical irregular q-difference equations ⋮ Local Galois group of irregular q-difference equations ⋮ Intrinsic Approach to Galois Theory of 𝑞-Difference Equations ⋮ Power series solutions of non-linear \(q\)-difference equations and the Newton-Puiseux polygon ⋮ Meromorphic solutions of linear \(q\)-difference equations ⋮ Generalized basic hypergeometric equations ⋮ Local analytic classification and local Galois theory of \(q\)-difference modules with non integral slopes ⋮ The variety of analytical classes of \(q\)-difference equations within a formal class ⋮ \(q\)-deformation of meromorphic solutions of linear differential equations ⋮ Galois theory of \(q\)-difference equations ⋮ Functional relations for solutions of \(q\)-difference equations ⋮ On \(q\)-summation and confluence ⋮ Galois theory of fuchsian q-difference equations ⋮ $q$-Conjugacy classes in loop groups ⋮ On the algebraic and analytic 𝑞-De Rham complexes attached to 𝑞-difference equations ⋮ On the archimedean and nonarchimedean 𝑞-Gevrey orders

Cites Work

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• On the calculation of some differential Galois groups
• On \(q\)- difference functional equations
• About the growth of entire functions solutions of linear algebraic \(q\)- difference equations
• Développements asymptotiques \(q\)-Gevrey et séries \(Gq\)-sommables. (\(q\)-Gevrey asymptotic expansions and \(Gq\)-summable series.)
• Galois theory of difference equations
• Arithmetic theory of \(q\)-difference equations. The \(q\)-analogue of Grothendieck-Katz's conjecture on \(p\)-curvatures
• Systèmes aux \(q\)-différences singuliers réguliers : classification, matrice de connexion et monodromie. (Regular singular \(q\)-difference systems: Classification, connection matrix and monodromy)
• Multisummability of formal power series solutions of linear analytic \(q\)-difference equations.
• Hasse-Arf filtrations and \(p\)-adic monodromy.
• Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin
• Categories tannakiennes
• Galois theory of fuchsian q-difference equations
• Linear algebraic groups.

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