Regular rings and perfectoid towers
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911721335029760 |
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| author | Hayashi, Kazuki |
| author_facet | Hayashi, Kazuki |
| contents | We prove a mixed-characteristic analogue of Kunz's theorem in terms of perfectoid towers: a Noetherian local ring of residue characteristic $p$ is regular if and only if it admits a flat map to a Noetherian ring that extends to a perfectoid tower. This result is deduced from another mixed-characteristic analogue due to O. Gabber and J. Lurie. We also characterize regularity for perfectoid towers via vanishing of single higher $\mathrm{Tor}$-module of the residue field with a perfectoid algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27337 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regular rings and perfectoid towers Hayashi, Kazuki Commutative Algebra 13H05, 14G45 We prove a mixed-characteristic analogue of Kunz's theorem in terms of perfectoid towers: a Noetherian local ring of residue characteristic $p$ is regular if and only if it admits a flat map to a Noetherian ring that extends to a perfectoid tower. This result is deduced from another mixed-characteristic analogue due to O. Gabber and J. Lurie. We also characterize regularity for perfectoid towers via vanishing of single higher $\mathrm{Tor}$-module of the residue field with a perfectoid algebra. |
| title | Regular rings and perfectoid towers |
| topic | Commutative Algebra 13H05, 14G45 |
| url | https://arxiv.org/abs/2605.27337 |