When does the F-signature exist?

Details When does the F-signature exist? When does the F-signature exist?

2005-02-16

arxiv.org/abs/math/0502351v1

Mathematics

Commutative Algebra

6 pages, to appear in Ann. Fac. Sci. Toulouse Math. (6)

Scientific paper

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.

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