Centers of perfectoid purity
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909789505716224 |
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| author | Fayolle, Anne |
| author_facet | Fayolle, Anne |
| contents | We introduce a mixed characteristic analog of log canonical centers in characteristic $0$ and centers of $F$-purity in positive characteristic, which we call centers of perfectoid purity. We show that their existence detects (the failure of) normality of the ring. We also show the existence of a special center of perfectoid purity that detects the perfectoid purity of $R$, analogously to the splitting prime of Aberbach and Enescu, and investigate its behavior under étale morphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Centers of perfectoid purity Fayolle, Anne Algebraic Geometry Commutative Algebra 14G45, 14F18, 14B05, 13A35 We introduce a mixed characteristic analog of log canonical centers in characteristic $0$ and centers of $F$-purity in positive characteristic, which we call centers of perfectoid purity. We show that their existence detects (the failure of) normality of the ring. We also show the existence of a special center of perfectoid purity that detects the perfectoid purity of $R$, analogously to the splitting prime of Aberbach and Enescu, and investigate its behavior under étale morphisms. |
| title | Centers of perfectoid purity |
| topic | Algebraic Geometry Commutative Algebra 14G45, 14F18, 14B05, 13A35 |
| url | https://arxiv.org/abs/2504.15569 |