Decomposition of de Rham complex for quasi-F-split varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909502067965952 |
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| author | Petrov, Alexander |
| author_facet | Petrov, Alexander |
| contents | Using the de Rham stack of Bhatt-Lurie and Drinfeld, we prove that de Rham complex of a smooth quasi-F-split variety over a perfect field of positive characteristic decomposes in all degrees. In particular, smooth proper quasi-F-split varieties have degenerate Hodge-to-de Rham spectral sequence, and satisfy Kodaira-Akizuki-Nakano vanishing. We apply this to prove that the Hodge-to-de Rham spectral sequence for the classifying stack of a reductive group over a field of positive characteristic degenerates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13356 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decomposition of de Rham complex for quasi-F-split varieties Petrov, Alexander Algebraic Geometry 14F40, 14G17 (Primary) 20G40 (Secondary) Using the de Rham stack of Bhatt-Lurie and Drinfeld, we prove that de Rham complex of a smooth quasi-F-split variety over a perfect field of positive characteristic decomposes in all degrees. In particular, smooth proper quasi-F-split varieties have degenerate Hodge-to-de Rham spectral sequence, and satisfy Kodaira-Akizuki-Nakano vanishing. We apply this to prove that the Hodge-to-de Rham spectral sequence for the classifying stack of a reductive group over a field of positive characteristic degenerates. |
| title | Decomposition of de Rham complex for quasi-F-split varieties |
| topic | Algebraic Geometry 14F40, 14G17 (Primary) 20G40 (Secondary) |
| url | https://arxiv.org/abs/2502.13356 |