Local monodromy of p-adic differential equations: an overview

Details Local monodromy of p-adic differential equations: an overview Local monodromy of p-adic differential equations: an overview

2005-01-22

arxiv.org/abs/math/0501361v2

preprint; published version: Intl J. Number Theory 1 (2005), 109-154.

Mathematics

Number Theory

45 pages; v2: refereed version, minor corrections; to appear in International Journal of Number Theory

Scientific paper

This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often with simpler proofs. These include Matsuda's classification of quasi-unipotent nabla-modules, the Christol-Mebkhout construction of the ramification filtration, and the Christol-Dwork Frobenius antecedent theorem. We also briefly discuss the p-adic local monodromy theorem without proof.

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