一个连通性导致积极的特征
A connectedness result in positive characteristic
摘要：
设$(R,m)$是一个正维数的完全局部环，它包含一个素特征的可分闭系数域。利用Peskine-Szpiro的消灭定理，Lyubeznik证明了局部上同调模$H^1_m(R)$的每一个元素都被Frobenius映射的迭代杀死当且仅当$R$的维数至少为2，并且它的删余谱在Zebraki拓扑中连通。我们给出了一个简单的证明这个定理和一个变化，更一般地说，产生的连通组件的数量。
英文摘要：
Let $(R,m)$ be a complete local ring of positive dimension, which contains a separably closed coefficient field of prime characteristic. Using a vanishing theorem of Peskine-Szpiro, Lyubeznik proved that every element of the local cohomology module $H^1_m(R)$ is killed by an iteration of the Frobenius map if and only if $R$ has dimension at least two and its punctured spectrum is connected in the Zariski topology. We give a simple proof of this theorem and of a variation which, more generally, yields the number of connected components.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
