Semistable reduction for overconvergent F -isocrystals on a curve
نویسنده
چکیده
Let X be a smooth affine curve over a field k of characteristic p > 0 and E an overconvergent F a-isocrystal on X for some positive integer a. We prove that after replacing k by some finite purely inseparable extension, there exists a finite separable morphism X ′ → X, the pullback of E along which extends to a log-F a-isocrystal on a smooth compactification of X . 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 André, Mebkhout and the author.
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