Slope filtration of quasi-unipotent overconvergent F-isocrystals

We study local properties of quasi-unipotent overconvergent F-isocrystals on a curve over a perfect field of positive characteristic p. For a phi-delta-module over the Robba ring R, we define the slope filtration for Frobenius structures. We prove that an overconvergent F-isocrystal is quasi-unipotent if and only if it has the slope filtration for Frobenius structures locally at every point on the complement of the curve.