La filtration canonique par les pentes d'un module aux q-différences et le gradué associé
arXiv:math/0210430
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