Lifting to truncated Brown-Peterson spectra and Hodge-de Rham degeneration in characteristic $p>0$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866908380729180160 |
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| author | Devalapurkar, Sanath K. |
| author_facet | Devalapurkar, Sanath K. |
| contents | The goal of this note is to prove that Hodge-de Rham degeneration holds for smooth and proper $\mathbf{F}_p$-schemes $X$ with $\dim(X)<p^n$ as soon as its category of quasicoherent sheaves admits a lift to the truncated Brown-Peterson spectrum $\mathrm{BP}\langle n-1\rangle$, and the Hochschild-Kostant-Rosenberg spectral sequence for $X$ degenerates at the $E_2$-page. This is obtained from a noncommutative version, whose proof is essentially the same as Mathew's argument in arXiv:1710.09045. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00739 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lifting to truncated Brown-Peterson spectra and Hodge-de Rham degeneration in characteristic $p>0$ Devalapurkar, Sanath K. Algebraic Topology Algebraic Geometry K-Theory and Homology The goal of this note is to prove that Hodge-de Rham degeneration holds for smooth and proper $\mathbf{F}_p$-schemes $X$ with $\dim(X)<p^n$ as soon as its category of quasicoherent sheaves admits a lift to the truncated Brown-Peterson spectrum $\mathrm{BP}\langle n-1\rangle$, and the Hochschild-Kostant-Rosenberg spectral sequence for $X$ degenerates at the $E_2$-page. This is obtained from a noncommutative version, whose proof is essentially the same as Mathew's argument in arXiv:1710.09045. |
| title | Lifting to truncated Brown-Peterson spectra and Hodge-de Rham degeneration in characteristic $p>0$ |
| topic | Algebraic Topology Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2303.00739 |