When does the F-signature exist?

Original · EN

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 N-graded ring at its irrelevant ideal or 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.