## Slope filtration of quasi-unipotent overconvergent $$F$$-isocrystals.(English)Zbl 0907.14007

The author studies Frobenius-crystals on the Robba ring, which can be thought of as a model for a (limit of) rigid analytic disks. These definition needs a Frobenius lift on the base but the resulting category is independent of that choice. One defines unipotent crystals as usual as successive extensions of constants objects, and quasi-unipotent means “unipotent after a finite covering”. The main result says that this is equivalent to having a slope-filtration. The theory is then applied to convergent and overconvergent $$F$$-isocrystals on curves.
Reviewer: G.Faltings (Bonn)

### MSC:

 14F30 $$p$$-adic cohomology, crystalline cohomology 14G20 Local ground fields in algebraic geometry 12H25 $$p$$-adic differential equations
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### References:

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