# ag.algebraic geometry – Isocrystals on simply connected varieties

This proves that there are no non-trivial convergent isocrystals on simply connected varieties. There is another similar result here, which basically implies the flat vector bundles on simply connected varieties are trivial. These are all special case of the de Jong’s conjecture that expects all isocrystals to be trivial with the assumption of simply connectedness(in char $$p$$). In all these papers the isocrystals are defined in the category of coherent sheaves, I was wondering whether these triviality results(conjectures) are(expected to be) true for quasi-coherent sheaves or not?