Esnault and Shiho - Convergent isocrystals on simply connected varieties proves that there are no non-trivial convergent isocrystals on simply connected varieties. There is another similar result in Esnault, Srinivas, and Bost - Simply connected varieties in characteristic $p > 0$, which basically implies the flat vector bundles on simply connected varieties are trivial. These are all special case of 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?
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3$\begingroup$ (Not related to your question, but I realize the "crystals" tag has no guidance about whether it refers to crystals in the sense of algebraic geometry, or in the sense of representation theory of Lie objects.) $\endgroup$– Sam HopkinsCommented Feb 23, 2021 at 0:31
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$\begingroup$ (I know less than nothing about the Lie theory side, but one idea would be to use crystalline-cohomology as a tag for AG instead of crystals.) $\endgroup$– Tabes BridgesCommented Feb 23, 2021 at 5:21
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