FINITE LOCAL MONODROMY OF OVERCONVERGENT UNIT-ROOT F-ISOCRYSTALS ON ACURVE

We prove that the category of p-adic continuous representations of a f undamental group of a curve over a perfect field of a positive charact eristic p with finite local monodromy is equivalent to that of overcon vergent unit-root F-isocrystals on the curve. To show the equivalence of categories, we study the local theory and apply it to the global ca se.