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It is conjectured by de Jong that, if is a connected smooth projective variety over an algebraically closed field of characteristic with trivial 'etale fundamental group, any isocrystal on on is trivial. We prove this conjecture under two additional assumptions. Version 2: the main change is an addendum. We prove that if is a connected smooth projective variety over an algebraically closed field of characteristic with trivial 'etale fundamental group, any infinitesimal isocrystal on is trivial. To this aim we wrote some general facts on such infinitesimal isocrystals over W which are missing in the literature.

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