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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2312.13456 |
| Etiquetas: |
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- We show that the Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails for threefolds in any positive characteristic, and for terminal 3-folds in characteristic $p \in \{2, 3, 5\}$. To prove this, we introduce the notion of $\mathbb{F}_p$-rationality for singularities in positive characteristic and we show that klt singularities in dimension at most 4 are $\mathbb{F}_p$-rational. We apply this to prove a Frobenius--stable version of the Kawamata--Viehweg vanishing theorem on $K$-trivial 3-folds.