  Given a smooth affine curve X over a field k of positive characteristic, and
an overconvergent F-isocrystal on X, we prove after replacing k by a finite
purely inseparable extension, there exists a finite separable cover of X, the
pullback of the isocrystal along which extends to a log-F-isocrystal on a
smooth compactification. This resolves a weak form of the global version of a
conjecture of Crew; the proof uses the local version of the conjecture,
established separately by Andre, Mebkhout and the author.
