The existence of the F-signature for rings with large Q-Gorenstein locus

JOURNAL OF ALGEBRA

卷:319

Article

Aberbach, Ian A.

关键词: F-signature;    tight closure;    Hilbert-Kunz multiplicity;    local cohomology;   

DOI  :  10.1016/j.jalgebra.2007.10.017

来源: Elsevier

【 摘 要 】

We show that the F-signature of a strongly F-regular local ring of characteristic p exists in the case that the non-Q-Gorenstein locus is dimension 1, given that a certain bound on zeroth local cohomology modules holds. This bound is shown to hold for rings essentially of finite type over a field. This is the first case in which hypotheses sufficient to prove the existence of the F-signature are not readily sufficient to prove the implication that weak F-regularity implies strong F-regularity. (C) 2007 Elsevier Inc. All rights reserved.

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