Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals
Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals
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DOI：
10.1016/j.jalgebra.2019.03.015
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发表时间：
2018-03
影响因子：
0.9
通讯作者：
Thomas Polstra;Pham Hung Quy
中科院分区：
文献类型：
--
作者：
Thomas Polstra;Pham Hung Quy
素特征局部环上的局部上同调模上的Frobenius作用的研究与紧闭包理论有着有趣的联系。本文通过发展局部上同调上的相对Frobenius作用的概念，建立了新的联系。作为应用，我们证明了一个环有F-幂零奇点当且仅当每个参数理想的紧闭包等于它的Frobenius闭包。
The study of Frobenius actions on local cohomology modules over a local ring of prime characteristic has interesting connections with the theory of tight closure. This paper establishes new connections by developing the notion of relative Frobenius actions on local cohomology. As an application, we show that a ring hasF-nilpotent singularities if and only if the tight closure of every parameter ideal is equal to its Frobenius closure.