On Quasi-$F$-Purity of Excellent Rings
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914059829379072 |
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| author | Jagathese, Vignesh |
| author_facet | Jagathese, Vignesh |
| contents | We introduce an analogue to Quasi-$F$-splittings, Quasi-$F$-purity, which is definable over rings that are not necessarily $F$-finite. We show that this property is equivalent to being Quasi-$F$-split in the complete local and $F$-finite case. We then exhibit that it is stable under completion, direct limit, and local/finite étale extension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10778 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Quasi-$F$-Purity of Excellent Rings Jagathese, Vignesh Commutative Algebra Algebraic Geometry 13A35 (Primary) 14B05 (Secondary) We introduce an analogue to Quasi-$F$-splittings, Quasi-$F$-purity, which is definable over rings that are not necessarily $F$-finite. We show that this property is equivalent to being Quasi-$F$-split in the complete local and $F$-finite case. We then exhibit that it is stable under completion, direct limit, and local/finite étale extension. |
| title | On Quasi-$F$-Purity of Excellent Rings |
| topic | Commutative Algebra Algebraic Geometry 13A35 (Primary) 14B05 (Secondary) |
| url | https://arxiv.org/abs/2503.10778 |