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

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).

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

Cited by in corpus (5)

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• On the Grothendieck conjecture on p-curvatures for q-difference equations
• 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
• Local analytic classification of $q$-difference equations with $|q|=1$
• Galois groups of the Lie-irreducible generalized $q$-hypergeometric equations of order three with $q$-real parameters : an approach using a density theorem