Effective generic freeness and applications to local cohomology

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-20 DOI:10.1112/jlms.12995

Yairon Cid-Ruiz, Ilya Smirnov

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引用次数: 0

Abstract

Let $A$ be a Noetherian domain and $R$ be a finitely generated $A$ -algebra. We study several features regarding the generic freeness over $A$ of an $R$ -module. For an ideal $I \subset R$ , we show that the local cohomology modules $H_{I}^{i} (R)$ are generically free over $A$ under certain settings where $R$ is a smooth $A$ -algebra. By utilizing the theory of Gröbner bases over arbitrary Noetherian rings, we provide an effective method to b make explicit the generic freeness over $A$ of a finitely generated $R$ -module.

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有效通用自由性及其在局部同调中的应用

假设 A $A$ 是诺特域，R $R$ 是有限生成的 A $A$ -代数。我们将研究 R $R$ 模块在 A $A$ 上的泛自由性的几个特征。对于一个理想 I ⊂ R $I （子集 R$），我们证明了局部同调模块 H I i ( R ) $\normalfont \text{H}_I^i(R)$ 在 R $R$ 是光滑的 A $A$ -代数的特定情况下在 A $A$ 上是泛自由的。通过利用任意诺特环上的格氏基理论，我们提供了一种有效的方法来明确有限生成的 R $R$ 模块在 A $A$ 上的泛自由性。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.