Periodicity of ideals of minors in free resolutions

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-04-14 DOI:10.1016/j.jalgebra.2025.04.004

Michael K. Brown , Hailong Dao , Prashanth Sridhar

引用次数: 0

Abstract

We study the asymptotic behavior of the ideals of minors in minimal free resolutions over local rings. In particular, we prove that such ideals are eventually 2-periodic over complete intersections and Golod rings. We also establish general results on the stable behavior of ideals of minors in any infinite minimal free resolution. These ideals have intimate connections to trace ideals and cohomology annihilators. Constraints on the stable values attained by the ideals of minors in many situations are obtained, and they can be explicitly computed in certain cases.

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自由解析度中小调理想的周期性

研究了局部环上最小自由分辨率下小子理想的渐近行为。特别地，我们证明了这些理想最终是在完全交点和gold环上的2周期的。我们还建立了在任意无限最小自由分辨率下，子点理想的稳定行为的一般结果。这些理想与迹理想和上同湮灭子有着密切的联系。在许多情况下，得到了未成年人理想所达到的稳定值的约束条件，在某些情况下，可以显式地计算出这些约束条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.