The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918519591927808 |
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| author | Baudin, Jefferson Bernasconi, Fabio Kawakami, Tatsuro |
| author_facet | Baudin, Jefferson Bernasconi, Fabio Kawakami, Tatsuro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13456 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails Baudin, Jefferson Bernasconi, Fabio Kawakami, Tatsuro Algebraic Geometry 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. |
| title | The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.13456 |