Grauert-Riemenschneider vanishing holds for F-pure threefolds in char p>5, implying Steenbrink vanishing for sharply F-pure pairs and logarithmic extension for one-forms.
Extending one-forms on $F$-regular singularities
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abstract
We prove the logarithmic extension theorem for one-forms on strongly $F$-regular singularities. Additionally, we establish the logarithmic extension theorem for one-forms on three-dimensional klt singularities in characteristic $p>41$. To this end, we reduce the problem to the logarithmic extension theorem for two-dimensional klt singularities with imperfect residue fields using a technique based on Cartier operators.
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math.AG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The paper surveys the theory of quasi-F-singularities and their relations to singularities in birational geometry.
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Local vanishing for F-pure threefolds
Grauert-Riemenschneider vanishing holds for F-pure threefolds in char p>5, implying Steenbrink vanishing for sharply F-pure pairs and logarithmic extension for one-forms.
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Quasi-$F$-singularities and singularities in birational geometry
The paper surveys the theory of quasi-F-singularities and their relations to singularities in birational geometry.