Study on p-adic cohomology, homotopy and overconvergent isocrystals

点击翻译按钮获取中文摘要

I proved the following results on overconvergent isocrystal, which is a certain p-adic differential equation. First, I proved the theorem of logarithmic extension for overconvergent isocrystals. Next I proved the theorem of cut-by-curves criterion for the log extendability of overconvergent isocrystals and the overconvergence of modules with integrable connections. Moreover, I proved a kind of purity theorem for overconvergent F-isocrystals. I defined the category of certain parabolic unit-root log convergent F-isocrystals and proved that it is equivalent to the category of tamely ramified p-adic representations of fundamental groups. Also, I proved a certain generalization of a result of Ogus-Vologodsky on the category of modules with integrable connection and the category of Higgs modules.