The F -signature and Strong F -regularity

  title={The F -signature and Strong F -regularity},
  author={GRAHAM J. LEUSCHKE},
  • Published 2002
We show that the F -signature of a local ring of characteristic p, defined by Huneke and Leuschke, is positive if and only if the ring is strongly F -regular. In [7], Huneke and Leuschke define the F -signature of an F -finite local ring of prime characteristic with perfect residue field. The F -signature, denoted s(R), is an asymptotic measure of the proportion of R-free direct summands in a direct-sum decomposition of R e , the ring of pth roots of R. This proportion seems to give subtle… CONTINUE READING

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