تقرير
The Brian\c{c}on-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras
| العنوان: | The Brian\c{c}on-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras |
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| المؤلفون: | Rodríguez-Villalobos, Sandra, Schwede, Karl |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Commutative Algebra, Mathematics - Algebraic Geometry, 13B22, 13A30, 13D22, 14B05, 13A35 |
| الوصف: | 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 Brian\c{c}on-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. Comment: 13 pages, comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.02433 |
| رقم الأكسشن: | edsarx.2406.02433 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |