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arXiv · 2310.06029

Twisting the Infinitesimal Site

Joshua Mundinger
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Abstract

We classify twistings of Grothendieck's differential operators on a smooth variety $X$ in prime characteristic $p$. We prove isomorphism classes of twistings are in bijection with $H^2(X,\mathbb{Z}_p(1))$, 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. 2024-08-23. Twisting the Infinitesimal Site. https://doi.org/10.1093/imrn%2Frnae186

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