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When does the F -signature exist?

Ian M. AberbachFlorian Enescu — 2006

Annales de la faculté des sciences de Toulouse Mathématiques

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.

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