Effective generic freeness and applications to local cohomology

IF 1 2区数学 Q1 MATHEMATICS Journal of the London Mathematical Society-Second Series 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

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.