A local-global correspondence for perfectoid purity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914553467502592 |
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| author | Ishizuka, Ryo Yoshikawa, Shou |
| author_facet | Ishizuka, Ryo Yoshikawa, Shou |
| contents | We introduce (lim-)perfectoid splitting, which is a global variant of (lim-)perfectoid purity. Our main result establishes a correspondence between the lim-perfectoid splitting of projective schemes and the lim-perfectoid purity of their Gorenstein section rings. As an application, we construct a new supply of examples of lim-perfectoid pure rings that go beyond the previously known complete intersection or splinter-type cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25265 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A local-global correspondence for perfectoid purity Ishizuka, Ryo Yoshikawa, Shou Algebraic Geometry Commutative Algebra Number Theory We introduce (lim-)perfectoid splitting, which is a global variant of (lim-)perfectoid purity. Our main result establishes a correspondence between the lim-perfectoid splitting of projective schemes and the lim-perfectoid purity of their Gorenstein section rings. As an application, we construct a new supply of examples of lim-perfectoid pure rings that go beyond the previously known complete intersection or splinter-type cases. |
| title | A local-global correspondence for perfectoid purity |
| topic | Algebraic Geometry Commutative Algebra Number Theory |
| url | https://arxiv.org/abs/2604.25265 |