论文标题
REES代数和主要特征的广义深度样条件
Rees algebras and generalized depth-like conditions in prime characteristic
论文作者
论文摘要
在本文中，我们解决了一个有关nilpotent Frobenius对Rees代数和相关分级环的问题。我们证明了Huneke定理对Cohen-Macaulay奇异性的nilpotent类似物。这是通过引入类似深度的不变式来实现的，该深度不变捕获了特殊案例lyubeznik的F-Depth和Maddox-Miller的广义F-Depth，并且与理想相关的广义深度有关。我们还描述了这种新不变式的几种属性，并确定了一类常规元素的弱f-nilpotence变形。
In this article we address a question concerning nilpotent Frobenius actions on Rees algebras and associated graded rings. We prove a nilpotent analog of a theorem of Huneke for Cohen-Macaulay singularities. This is achieved by introducing a depth-like invariant which captures as special cases Lyubeznik's F-depth and the generalized F-depth from Maddox-Miller and is related to the generalized depth with respect to an ideal. We also describe several properties of this new invariant and identify a class of regular elements for which weak F-nilpotence deforms.
