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arXiv · 2506.23526

A note on cohomological boundedness for $F$-divided sheaves and $\mathcal{D}$-modules

Xiaodong Yi
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Abstract

Let $X$ be a smooth proper scheme over an algebraically closed field $k$ in characteristic $p$. In this short note, by interpreting $\mathcal{D}_{X}$-modules as $F$-divided sheaves and establishing a cohomological boundedness property for $F$-divided sheaves, we prove that any $\mathcal{O}_{X}$-coherent $\mathcal{D}_{X}$-module has finite dimensional $\mathcal{D}_{X}$-module cohomology.

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Xiaodong Yi. 2025-06-30. A note on cohomological boundedness for $F$-divided sheaves and $\mathcal{D}$-modules. https://arxiv.org/abs/2506.23526

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