$F$-injectivity does not imply $F$-fullness in normal domains
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917325446316032 |
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| author | De Stefani, Alessandro Polstra, Thomas Simpson, Austyn |
| author_facet | De Stefani, Alessandro Polstra, Thomas Simpson, Austyn |
| contents | We construct examples of noetherian three-dimensional local geometrically normal domains of prime characteristic which are $F$-injective but not $F$-full. Along the way, we find examples of two-dimensional local geometrically normal domains which are $F$-injective but not $F$-anti-nilpotent. A crucial theme of our constructions is the behavior of $F$-injectivity along a purely inseparable finite base change. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $F$-injectivity does not imply $F$-fullness in normal domains De Stefani, Alessandro Polstra, Thomas Simpson, Austyn Commutative Algebra We construct examples of noetherian three-dimensional local geometrically normal domains of prime characteristic which are $F$-injective but not $F$-full. Along the way, we find examples of two-dimensional local geometrically normal domains which are $F$-injective but not $F$-anti-nilpotent. A crucial theme of our constructions is the behavior of $F$-injectivity along a purely inseparable finite base change. |
| title | $F$-injectivity does not imply $F$-fullness in normal domains |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2506.00646 |