When does the F-signature exist?
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 2, p. 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.

@article{AFST_2006_6_15_2_195_0,
     author = {Aberbach, Ian M. and Enescu, Florian},
     title = {When does the $F$-signature exist?},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 15},
     number = {2},
     year = {2006},
     pages = {195-201},
     doi = {10.5802/afst.1118},
     mrnumber = {2244213},
     zbl = {1118.13003},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2006_6_15_2_195_0}
}
Aberbach, Ian M.; Enescu, Florian. When does the $F$-signature exist?. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 2, pp. 195-201. doi : 10.5802/afst.1118. http://www.numdam.org/item/AFST_2006_6_15_2_195_0/

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