A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866915701831237632 |
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| author | Nakazato, Kei Shimomoto, Kazuma |
| author_facet | Nakazato, Kei Shimomoto, Kazuma |
| contents | In this paper, we prove that a complete Noetherian local domain of mixed characteristic $p>0$ with perfect residue field has an integral extension that is an integrally closed, almost Cohen-Macaulay domain such that the Frobenius map is surjective modulo $p$. This result is seen as a mixed characteristic analogue of the fact that the perfect closure of a complete local domain in positive characteristic is almost Cohen-Macaulay. To this aim, we carry out a detailed study of decompletion of perfectoid rings and establish the Witt-perfect (decompleted) version of André's perfectoid Abhyankar's lemma and Riemann's extension theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_03512 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras Nakazato, Kei Shimomoto, Kazuma Commutative Algebra Algebraic Geometry Number Theory In this paper, we prove that a complete Noetherian local domain of mixed characteristic $p>0$ with perfect residue field has an integral extension that is an integrally closed, almost Cohen-Macaulay domain such that the Frobenius map is surjective modulo $p$. This result is seen as a mixed characteristic analogue of the fact that the perfect closure of a complete local domain in positive characteristic is almost Cohen-Macaulay. To this aim, we carry out a detailed study of decompletion of perfectoid rings and establish the Witt-perfect (decompleted) version of André's perfectoid Abhyankar's lemma and Riemann's extension theorem. |
| title | A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras |
| topic | Commutative Algebra Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2002.03512 |