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arXiv · 2604.14760

Local vanishing for F-pure threefolds

Tatsuro Kawakami
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Abstract

We establish Grauert--Riemenschneider vanishing for $F$-pure threefolds over a perfect field $k$ of characteristic $p>5$. We apply this to prove Steenbrink vanishing for three-dimensional sharply $F$-pure pairs in characteristic $p>5$. As a consequence, we obtain the logarithmic extension for one-forms in this setting.

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Tatsuro Kawakami. 2026-04-16. Local vanishing for F-pure threefolds. https://arxiv.org/abs/2604.14760

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