On a Positive Equicharacteristic Variant of the p-Curvature Conjecture

Our aim is to formulate and prove a weak form in equal characteristic $p>0$ of the $p$-curvature conjecture. We also show the existence of a counterexample to a strong form of it.

2010 Mathematics Subject Classification: 14D05, 14E20, 14F35, 11G10, 11G99

Keywords and Phrases: varieties in positive characteristic, stratified bundles, étale trivializable bundles, monodromy group, abelian varieties

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