La filtration canonique par les pentes d'un module aux q-différences

According to Adams' lemma, to the first slope of the Newton polygon of a q-difference equation is associated a full complement of convergent solutions. We draw from this the existence of a canonical filtration by the slopes of q-difference modules, such that the associated graded module functor is faithful, exact and tensor compatible. To cite this article: J. Sauloy, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 11–14