D-模算术的整体论与F-isocristaux超收敛性
Sur l'holonomie de D-modules arithmétiques associés à des F-isocristaux surconvergents sur des courbes lisses
摘要：
我们证明了在平滑曲线上过收敛F-等晶的算术D-模是完整的。利用幂幺F-等晶来自对数F-等晶的事实，证明了幂幺F-等晶是完整D-模。我们从Matsuda-Trihan曲线上的F-同晶的半稳定定理推导出一般情况，该定理依赖于André，Kedlaya和Mebkhout独立证明的p-adic monodromy定理。主要结果已被D.卡罗
英文摘要：
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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