The Briançon-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917767822704640 |
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| author | Rodríguez-Villalobos, Sandra Schwede, Karl |
| author_facet | Rodríguez-Villalobos, Sandra Schwede, Karl |
| contents | We prove that, given a sufficiently functorial assignment from rings to big Cohen-Macaulay algebras $R \mapsto B$, that the associated big Cohen-Macaulay closure operation on ideals $I \mapsto I B \cap R$ necessarily satisfies the Briançon-Skoda type property. The proof combines arguments of Lipman-Teissier, Hochster, Ma, and Hochster-Huneke. Specializing to mixed characteristic, and utilizing a result of Bhatt on absolute integral closures, this recovers a slight strengthening of a result of Heitmann. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Briançon-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras Rodríguez-Villalobos, Sandra Schwede, Karl Commutative Algebra Algebraic Geometry 13B22, 13A30, 13D22, 14B05, 13A35 We prove that, given a sufficiently functorial assignment from rings to big Cohen-Macaulay algebras $R \mapsto B$, that the associated big Cohen-Macaulay closure operation on ideals $I \mapsto I B \cap R$ necessarily satisfies the Briançon-Skoda type property. The proof combines arguments of Lipman-Teissier, Hochster, Ma, and Hochster-Huneke. Specializing to mixed characteristic, and utilizing a result of Bhatt on absolute integral closures, this recovers a slight strengthening of a result of Heitmann. |
| title | The Briançon-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras |
| topic | Commutative Algebra Algebraic Geometry 13B22, 13A30, 13D22, 14B05, 13A35 |
| url | https://arxiv.org/abs/2406.02433 |