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We introduce twisted differential calculus of negative level and prove adescent theorem: Frobenius pullback provides an equivalence between finitelypresented modules endowed with a topologically quasi-nilpotent twistedconnection of level minus one and those of level zero. We explain how this isrelated to the existence of a Cartier operator on prismatic crystals. For thesake of readability, we limit ourselves to the case of dimension one.

Twisted differential operators of negative level and prismatic crystals