Almost Cohen-Macaulay algebras in mixed characteristic via Fontaine rings
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arXiv
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| Format: | Preprint |
| Publié: |
2010
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| _version_ | 1866918374229934080 |
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| author | Shimomoto, Kazuma |
| author_facet | Shimomoto, Kazuma |
| contents | In the present paper, it is proved that any complete local domain of mixed characteristic has a weakly almost Cohen-Macaulay algebra in the sense that some system of parameters is a weakly almost regular sequence, which is a notion defined via a valuation. The central idea of this result originates from the main statement obtained by Heitmann to prove the Monomial Conjecture in dimension 3. In fact, A weakly almost Cohen-Macaulay algebra is constructed over the absolute integral closure of a complete local domain by applying the methods of Fontaine rings and Witt vectors. A connection of the main theorem with the Monomial Conjecture is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1005_3275 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Almost Cohen-Macaulay algebras in mixed characteristic via Fontaine rings Shimomoto, Kazuma Commutative Algebra Algebraic Geometry In the present paper, it is proved that any complete local domain of mixed characteristic has a weakly almost Cohen-Macaulay algebra in the sense that some system of parameters is a weakly almost regular sequence, which is a notion defined via a valuation. The central idea of this result originates from the main statement obtained by Heitmann to prove the Monomial Conjecture in dimension 3. In fact, A weakly almost Cohen-Macaulay algebra is constructed over the absolute integral closure of a complete local domain by applying the methods of Fontaine rings and Witt vectors. A connection of the main theorem with the Monomial Conjecture is also discussed. |
| title | Almost Cohen-Macaulay algebras in mixed characteristic via Fontaine rings |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/1005.3275 |