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.
Extendability of differential forms via Cartier operators.https: //arxiv.org/abs/2207.13967v4
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Proves logarithmic extension of one-forms on strongly F-regular singularities and on 3D klt singularities in char p>41 by reducing via Cartier operators to the 2D klt case with imperfect residue fields.
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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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Extending one-forms on $F$-regular singularities
Proves logarithmic extension of one-forms on strongly F-regular singularities and on 3D klt singularities in char p>41 by reducing via Cartier operators to the 2D klt case with imperfect residue fields.