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We complete our proof that given an overconvergent F-isocrystal on a varietyover a field of positive characteristic, one can pull back along a suitablegenerically finite cover to obtain an isocrystal which extends, withlogarithmic singularities and nilpotent residues, to some complete variety. Wealso establish an analogue for F-isocrystals overconvergent inside a partialcompactification. By previous results, this reduces to solving a local problemin a neighborhood of a valuation of height 1 and residual transcendence degree0. We do this by studying the variation of some numerical invariants attachedto p-adic differential modules, analogous to the irregularity of a complexmeromorphic connection. This allows for an induction on the transcendencedefect of the valuation, i.e., the discrepancy between the dimension of thevariety and the rational rank of the valuation.

Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations