On deformation of perfectoid purity in Gorenstein domains
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915298466070528 |
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| author | Baily, Benjamin Dovgodko, Karina Simpson, Austyn Westbrook, Jack |
| author_facet | Baily, Benjamin Dovgodko, Karina Simpson, Austyn Westbrook, Jack |
| contents | If $(R,\mathfrak{m})$ is a complete local ring of mixed characteristic $(0,p)$ and $R/pR$ is an $F$-pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid pure. This condition is related to the Cohen-Macaulayness of the absolute integral closures of Gorenstein local domains of mixed characteristic which are not necessarily excellent. Along the way, we show that the problem of lifting $F$-purity of $R/pR$ to perfectoid purity of $R$ is equivalent to a similar deformation problem for the splinter property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On deformation of perfectoid purity in Gorenstein domains Baily, Benjamin Dovgodko, Karina Simpson, Austyn Westbrook, Jack Commutative Algebra If $(R,\mathfrak{m})$ is a complete local ring of mixed characteristic $(0,p)$ and $R/pR$ is an $F$-pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid pure. This condition is related to the Cohen-Macaulayness of the absolute integral closures of Gorenstein local domains of mixed characteristic which are not necessarily excellent. Along the way, we show that the problem of lifting $F$-purity of $R/pR$ to perfectoid purity of $R$ is equivalent to a similar deformation problem for the splinter property. |
| title | On deformation of perfectoid purity in Gorenstein domains |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2504.02966 |