We classify twistings of Grothendieck’s differential operators on a smooth variety X in prime characteristic p. We prove that isomorphism classes of twistings are in bijection with H²(X,Zₚ(1)), the degree 2, weight 1 syntomic cohomology of X. We also discuss the relationship between twistings of crystalline and Grothendieck differential operators. Twistings in mixed characteristic are also analyzed.
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Joshua Mundinger (2024) studied this question.
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