The F-signature and strong F-regularity
英文摘要:
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.
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。
Ian M. Aberbach, Graham J. Leuschke
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.
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。
继续探索
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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The $F$-signature of a local ring of prime characteristic is a numerical invariant that detects many interesting properties. For example, this invariant detects (non)singularity and strong $F$-regularity. However, it is very difficult to compute. Motivated by different aspects of the $F$-signature, we define a numerical invariant for rings of characteristic zero or $p>0$ that exhibits many of the useful properties of the $F$-signature. We also compute many examples of this invariant, including cases where the $F$-signature is not known. We also obtain a number of results on symbolic powers and…
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