F签名何时存在？
When does the F-signature exist?
摘要：
证明了特征p >0的F-有限局部环R的F-签名存在于R是$\mathbf{N}$ -分次环在其无关理想上的局部化或$\mathbf{Q}$ -Gorenstein在其删余谱上的局部化.这推广了Huneke，Leuschke，Yao和Singh的结果，并在弱F-正则性等价于强F-正则性的情况下证明了F-签名的存在性。
英文摘要：
We show that the F-signature of an F-finite local ring R of characteristic p >0 exists when R is either the localization of an $\mathbf{N}$-graded ring at its irrelevant ideal or $\mathbf{Q}$-Gorenstein on its punctured spectrum. This extends results by Huneke, Leuschke, Yao and Singh and proves the existence of the F-signature in the cases where weak F-regularity is known to be equivalent to strong F-regularity.
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。
