Galois theory of fuchsian q-difference equations

DOI10.1016/j.ansens.2002.10.001zbMath1053.39033arXivmath/0210221OpenAlexW2029074853MaRDI QIDQ4470743

Jacques Sauloy

Publication date: 15 June 2004

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210221

zbMATH Keywords

Galois groupsRiemann-Hilbert correspondence\(q\)-difference equationTannaka dualitydensity theorem

Mathematics Subject Classification ID

Difference equations, scaling ((q)-differences) (39A13) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34) General theory of difference equations (39A05) Difference algebra (12H10)

Related Items (22)

On classical irregular q-difference equations ⋮ The canonical filtration by the slopes of a \(q\)-difference module and the associated graded module. ⋮ A modular-type formula for \((x;q)_\infty \) ⋮ Local Galois group of irregular q-difference equations ⋮ The space of monodromy data for the Jimbo-Sakai family of \(q\)-difference equations ⋮ An elliptic Garnier system ⋮ Intrinsic Approach to Galois Theory of 𝑞-Difference Equations ⋮ Formal confluence of quantum differential operators ⋮ An algorithm to recognize regular singular Mahler systems ⋮ A Galois \(D\)-groupoid for \(q\)-difference equations ⋮ Asymptotic behaviours of \(q\)-orthogonal polynomials from a \(q\)-Riemann Hilbert problem ⋮ Generalized basic hypergeometric equations ⋮ Local analytic classification and local Galois theory of \(q\)-difference modules with non integral slopes ⋮ Equivariant hom-Lie algebras and twisted derivations on (arithmetic) schemes ⋮ A local Galois \(D\)-groupoid for Fuchsian \(q\)-difference systems ⋮ Multiplicity and vanishing lemmas for differential and \(q\)-difference equations in the Siegel-Shidlovsky theory ⋮ Galois theory of \(q\)-difference equations ⋮ Galois theories of \(q\)-difference equations: comparison theorems ⋮ Commutation relations and discrete garnier systems ⋮ Elliptic \((p,q)\)-difference modules ⋮ Quantum \(K\)-theory and \(q\)-difference equations ⋮ The canonical slope filtration of a \(q\)-difference module

Cites Work

• On the calculation of some differential Galois groups
• About the growth of entire functions solutions of linear algebraic \(q\)- difference equations
• 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)
• The canonical slope filtration of a \(q\)-difference module
• The canonical filtration by the slopes of a \(q\)-difference module and the associated graded module.
• Equations différentielles à points singuliers réguliers
• Différentielles non commutatives et théorie de Galois différentielle ou aux différences
• Conjugacy classes in loop groups and G-bundles on elliptic curves
• Local analytic classification of q-difference equations
• Linear algebraic groups.
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