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\(F\)-isocrystals and their monodromy groups. (English) Zbl 0783.14008
The paper provides some facts about monodromy-groups of convergent and overconvergent \(F\)-isocrystals. The main technical tools are the study of unit root crystals, and the structure of rank-one overconvergent crystals on a curve. The main result is an overconvergent analogue of Deligne’s theory of determinated weights.

MSC:
14F30 \(p\)-adic cohomology, crystalline cohomology
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