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Main Author: Yi, Xiaodong
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.23526
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author Yi, Xiaodong
author_facet Yi, Xiaodong
contents 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.
format Preprint
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institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A note on cohomological boundedness for $F$-divided sheaves and $\mathcal{D}$-modules
Yi, Xiaodong
Algebraic Geometry
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.
title A note on cohomological boundedness for $F$-divided sheaves and $\mathcal{D}$-modules
topic Algebraic Geometry
url https://arxiv.org/abs/2506.23526