Integral perfectoid big Cohen-Macaulay algebras via André's theorem
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arXiv
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866915824777822208 |
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| author | Shimomoto, Kazuma |
| author_facet | Shimomoto, Kazuma |
| contents | The main result of this article is to prove that any Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen-Macaulay algebra. The proof of this result is based on the construction of almost Cohen-Macaulay algebras in mixed characteristic due to Yves André. Moreover, we prove that the absolute integral closure of a complete Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen-Macaulay algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1706_06946 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Integral perfectoid big Cohen-Macaulay algebras via André's theorem Shimomoto, Kazuma Commutative Algebra Algebraic Geometry The main result of this article is to prove that any Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen-Macaulay algebra. The proof of this result is based on the construction of almost Cohen-Macaulay algebras in mixed characteristic due to Yves André. Moreover, we prove that the absolute integral closure of a complete Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen-Macaulay algebra. |
| title | Integral perfectoid big Cohen-Macaulay algebras via André's theorem |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/1706.06946 |