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arXiv · 0705.0416

Sur l'holonomie de D-modules arithmétiques associés à des F-isocristaux surconvergents sur des courbes lisses

Christine Noot-Huyghe·Fabien Trihan
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Abstract

We show that the arithmetic D-module associated to an overconvergent F-isocrystal over a smooth curve is holonomic. We first prove that unipotent F-isocrystals are holonomic D-module by using the fact that such F-isocrystals come from logarithmic F-isocrystals. We deduce the general case from the semi-stable theorem for F-isocrystals over curves of Matsuda-Trihan which relies on the p-adic monodromy theorem independently proved by André, Kedlaya and Mebkhout. The main result has already been proved by D. Caro.

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Christine Noot-Huyghe, Fabien Trihan. 2007-07-05. Sur l'holonomie de D-modules arithmétiques associés à des F-isocristaux surconvergents sur des courbes lisses. https://arxiv.org/abs/0705.0416

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