"The authors reconsider M. J. Rothstein’s axiomatization [Trans. Amer. Math. Soc. 297 (1986), no. 1, 159–180; MR0849473 (87m:58015)] of supermanifolds in the light of its giving a much wider category of supermanifolds than the Berezin-Leıtes-Kostant category of supermanifolds for a given choice of the Banach algebra occurring as the base. They show that by adding an axiom asserting the completeness of the rings of sections of structure sheaves this difficulty can be removed. Moreover, when the base algebra is a finite-dimensional exterior algebra, then the category of Rothstein supermanifolds is equivalent to the category of G-supermanifolds introduced by Bartocci, Bruzzo and Hernández Ruipérez [The geometry of supermanifolds, Kluwer Dordrecht, 1991]." J. S. Joel, MR1153267 (92k:58015)
An axiomatic approach to supermanifolds
BARTOCCI, CLAUDIO;
1992-01-01
Abstract
"The authors reconsider M. J. Rothstein’s axiomatization [Trans. Amer. Math. Soc. 297 (1986), no. 1, 159–180; MR0849473 (87m:58015)] of supermanifolds in the light of its giving a much wider category of supermanifolds than the Berezin-Leıtes-Kostant category of supermanifolds for a given choice of the Banach algebra occurring as the base. They show that by adding an axiom asserting the completeness of the rings of sections of structure sheaves this difficulty can be removed. Moreover, when the base algebra is a finite-dimensional exterior algebra, then the category of Rothstein supermanifolds is equivalent to the category of G-supermanifolds introduced by Bartocci, Bruzzo and Hernández Ruipérez [The geometry of supermanifolds, Kluwer Dordrecht, 1991]." J. S. Joel, MR1153267 (92k:58015)
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