Computation method for perfectoid purity and perfectoid BCM-regularity
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915458655977472 |
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| author | Yoshikawa, Shou |
| author_facet | Yoshikawa, Shou |
| contents | In this paper, we introduce the notion of quasi-$F$-splitting for rings in mixed characteristic. By comparing quasi-$F$-splitting with perfectoid purity, we obtain a new inversion of adjunction-type result. Furthermore, we study the possible values of the perfectoid pure threshold of $\mathrm{div}(p)$ and construct new examples of perfectoid pure rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computation method for perfectoid purity and perfectoid BCM-regularity Yoshikawa, Shou Algebraic Geometry In this paper, we introduce the notion of quasi-$F$-splitting for rings in mixed characteristic. By comparing quasi-$F$-splitting with perfectoid purity, we obtain a new inversion of adjunction-type result. Furthermore, we study the possible values of the perfectoid pure threshold of $\mathrm{div}(p)$ and construct new examples of perfectoid pure rings. |
| title | Computation method for perfectoid purity and perfectoid BCM-regularity |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.06108 |