## On a positive equicharacteristic variant of the $p$-curvature conjecture

### Summary

Summary: 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.

### Mathematics Subject Classification

14D05, 14E20, 14F35, 11G10, 11G99

### Keywords/Phrases

varieties in positive characteristic, stratified bundles, étale trivializable bundles, monodromy group, abelian varieties