Localization functors and cosupport in derived categories of commutative Noetherian rings
| العنوان: | Localization functors and cosupport in derived categories of commutative Noetherian rings |
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| المؤلفون: | Yuji Yoshino, Tsutomu Nakamura |
| المصدر: | Pacific Journal of Mathematics. 296:405-435 |
| بيانات النشر: | Mathematical Sciences Publishers, 2018. |
| سنة النشر: | 2018 |
| مصطلحات موضوعية: | Noetherian, Pure mathematics, Noetherian ring, Functor, Generalization, General Mathematics, 010102 general mathematics, Dimension (graph theory), Commutative Algebra (math.AC), Mathematics - Commutative Algebra, 01 natural sciences, 13D09, 13D45, 55P60, Mathematics - Algebraic Geometry, Mathematics::K-Theory and Homology, Mathematics::Category Theory, 0103 physical sciences, FOS: Mathematics, 010307 mathematical physics, Krull dimension, Finitely-generated abelian group, 0101 mathematics, Algebraic Geometry (math.AG), Commutative property, Mathematics |
| الوصف: | Let $R$ be a commutative Noetherian ring. We introduce the notion of localization functors $\lambda^W$ with cosupports in arbitrary subsets $W$ of $\text{Spec}\, R$; it is a common generalization of localizations with respect to multiplicatively closed subsets and left derived functors of ideal-adic completion functors. We prove several results about the localization functors $\lambda^W$, including an explicit way to calculate $\lambda^W$ by the notion of Cech complexes. As an application, we can give a simpler proof of a classical theorem by Gruson and Raynaud, which states that the projective dimension of a flat $R$-module is at most the Krull dimension of $R$. As another application, it is possible to give a functorial way to replace complexes of flat $R$-modules or complexes of finitely generated $R$-modules by complexes of pure-injective $R$-modules. Comment: 26 pages, to appear in Pacific J. Math |
| تدمد: | 0030-8730 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd6148c90ea7e24171b71387f56db63d https://doi.org/10.2140/pjm.2018.296.405 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....dd6148c90ea7e24171b71387f56db63d |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 00308730 |
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