Feuilleter
no. 2
When does the F-signature exist?
Ian M. Aberbach1 ; Florian Enescu2
1 Department of Mathematics, University of Missouri, Columbia, MO 65211.
2 Department of Mathematics and Statistics, Georgia State University, Atlanta, 30303 and The Institute of Mathematics of the Romanian Academy (Romania).
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 15 (2006) no. 2, pp. 195-201

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.

Nous prouvons dans cet article l’existence de la F-signature d’un anneau local F-fini R, de caractéristique positive p, quand R est la localisation à l’unique idéal homogène maximal d’un anneau N-gradué ou quand R est Q-Gorenstein sur son spectre épointé. Ceci généralise les résultats de Huneke, Leuschke, Yao et Singh et prouve l’existence de la F-signature dans les cas où faible et forte F-régularité sont équivalentes.

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Accepté le :
Publié le :
DOI : 10.5802/afst.1118

Ian M. Aberbach 1 ; Florian Enescu 2

1 Department of Mathematics, University of Missouri, Columbia, MO 65211.
2 Department of Mathematics and Statistics, Georgia State University, Atlanta, 30303 and The Institute of Mathematics of the Romanian Academy (Romania). 
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Ian M. Aberbach; Florian Enescu. When does the $F$-signature exist?. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 15 (2006) no. 2, pp. 195-201. doi: 10.5802/afst.1118

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