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

Jacques Sauloy
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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).

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Jacques Sauloy. 2002-10-28. La filtration canonique par les pentes d'un module aux q-différences et le gradué associé. https://arxiv.org/abs/math/0210430

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