Prismatic Kunz's theorem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911399858405376 |
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| author | Ishizuka, Ryo Nakazato, Kei |
| author_facet | Ishizuka, Ryo Nakazato, Kei |
| contents | In this paper, we prove "prismatic Kunz's theorem" which states that a complete Noetherian local ring $R$ of residue characteristic $p$ is a regular local ring if and only if the Frobenius lift on a prismatic complex of (a derived enhancement of) $R$ over a specific prism $(A, I)$ is faithfully flat. This generalizes classical Kunz's theorem from the perspective of extending the "Frobenius map" to mixed characteristic rings. Our approach involves studying the deformation problem of the "regularity" of prisms and demonstrating the faithful flatness of the structure map of the prismatic complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06207 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prismatic Kunz's theorem Ishizuka, Ryo Nakazato, Kei Commutative Algebra Algebraic Geometry Number Theory In this paper, we prove "prismatic Kunz's theorem" which states that a complete Noetherian local ring $R$ of residue characteristic $p$ is a regular local ring if and only if the Frobenius lift on a prismatic complex of (a derived enhancement of) $R$ over a specific prism $(A, I)$ is faithfully flat. This generalizes classical Kunz's theorem from the perspective of extending the "Frobenius map" to mixed characteristic rings. Our approach involves studying the deformation problem of the "regularity" of prisms and demonstrating the faithful flatness of the structure map of the prismatic complex. |
| title | Prismatic Kunz's theorem |
| topic | Commutative Algebra Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2402.06207 |