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

2002/10/28 by Jacques Sauloy, Sauloy, Jacques
Mathematics · #05A30 - 12H10 - 39A13 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:05A30 #msc:12H10 #msc:39A13

paper · pdf · doi:10.48550/arxiv.math/0210430

47 pages. Prepublication du Laboratoire Emile Picard n.249. See also http://picard.ups-tlse.fr

arxiv created 2002/10/28 · arxiv updated 2009/11/30

Abstract

We show that the Newton polygon of a linear q-difference equation depends only on the corresponding q-difference module. We interpret the classical results of convergent factorisation of Adams-Birkhoff-Guenther in terms of the existence of a canonical filtration. Moreover, the associated graded module has excellent functorial (resp. tensorial) properties, whence its interest for classification (resp. for Galois theory).

Related

• Théorie analytique locale des équations aux q-différences de pentes arbitraires
• Classification de modules aux différences filtrés isogradués
• Systèmes aux q-différences singuliers réguliers: solutions canoniques, classification, matrice de connexion et monodromie
• 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
• Parameterized generic Galois groups for q-difference equations, followed by the appendix "The Galois D-groupoid of a q-difference system" by Anne Granier