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Slope filtration of quasi-unipotent overconvergent F -isocrystals

Nobuo Tsuzuki — 1998

Annales de l'institut Fourier

We study local properties of quasi-unipotent overconvergent F -isocrystals on a curve over a perfect field of positive characteristic p . For a φ - -module over the Robba ring , 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.

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