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arXiv · 2303.07373

Hochschild cohomology of differential operators in positive characteristic

Joshua Mundinger
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Abstract

For $k$ a field of positive characteristic and $X$ a smooth variety over $k$, we compute the Hochschild cohomology of Grothendieck's differential operators on $X$. The answer involves the derived inverse limit of the Frobenius acting on the cohomology of the structure sheaf of $X$.

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Joshua Mundinger. 2023-03-13. Hochschild cohomology of differential operators in positive characteristic. https://doi.org/10.1016/j.jalgebra.2024.03.032

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