  We complete our proof that given an overconvergent F-isocrystal on a variety
over a field of positive characteristic, one can pull back along a suitable
generically finite cover to obtain an isocrystal which extends, with
logarithmic singularities and nilpotent residues, to some complete variety. We
also establish an analogue for F-isocrystals overconvergent inside a partial
compactification. By previous results, this reduces to solving a local problem
in a neighborhood of a valuation of height 1 and residual transcendence degree
0. We do this by studying the variation of some numerical invariants attached
to p-adic differential modules, analogous to the irregularity of a complex
meromorphic connection. This allows for an induction on the transcendence
defect of the valuation, i.e., the discrepancy between the dimension of the
variety and the rational rank of the valuation.
