We show that the -signature of an -finite local ring of characteristic exists when is either the localization of an -graded ring at its irrelevant ideal or -Gorenstein on its punctured spectrum. This extends results by Huneke, Leuschke, Yao and Singh and proves the existence of the -signature in the cases where weak -regularity is known to be equivalent to strong -regularity.
Nous prouvons dans cet article l’existence de la -signature d’un anneau local -fini , de caractéristique positive , quand est la localisation à l’unique idéal homogène maximal d’un anneau -gradué ou quand est -Gorenstein sur son spectre épointé. Ceci généralise les résultats de Huneke, Leuschke, Yao et Singh et prouve l’existence de la -signature dans les cas où faible et forte -régularité sont équivalentes.
@article{AFST_2006_6_15_2_195_0,
author = {Ian M. Aberbach and Florian Enescu},
title = {When does the $F$-signature exist?},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {195--201},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 15},
number = {2},
year = {2006},
doi = {10.5802/afst.1118},
mrnumber = {2244213},
zbl = {1118.13003},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1118/}
}
TY - JOUR AU - Ian M. Aberbach AU - Florian Enescu TI - When does the $F$-signature exist? JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2006 SP - 195 EP - 201 VL - 15 IS - 2 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1118/ DO - 10.5802/afst.1118 LA - en ID - AFST_2006_6_15_2_195_0 ER -
%0 Journal Article %A Ian M. Aberbach %A Florian Enescu %T When does the $F$-signature exist? %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2006 %P 195-201 %V 15 %N 2 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1118/ %R 10.5802/afst.1118 %G en %F AFST_2006_6_15_2_195_0
Ian M. Aberbach; Florian Enescu. 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. https://afst.centre-mersenne.org/articles/10.5802/afst.1118/
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