We discuss an axiomatic approach to supermanifolds valid for arbitrary ground graded commutative Banach algebras B. Rothstein’s axiomatics is revisited and completed by a further requirement which calls for the completeness of the rings of sections of the structure sheaves, and allows one to dispose of some undesirable features of Rothstein supermanifolds. The ensuing system of axioms determines a category of supermanifolds which coincides with graded manifolds when B = R, and with G-supermanifolds when B is a finite-dimensional exterior algebra. This category is studied in detail. The case of holomorphic supermanifolds is also outlined.
Foundations of supermanifold theory: the axiomatic approach
BARTOCCI, CLAUDIO;
1993-01-01
Abstract
We discuss an axiomatic approach to supermanifolds valid for arbitrary ground graded commutative Banach algebras B. Rothstein’s axiomatics is revisited and completed by a further requirement which calls for the completeness of the rings of sections of the structure sheaves, and allows one to dispose of some undesirable features of Rothstein supermanifolds. The ensuing system of axioms determines a category of supermanifolds which coincides with graded manifolds when B = R, and with G-supermanifolds when B is a finite-dimensional exterior algebra. This category is studied in detail. The case of holomorphic supermanifolds is also outlined.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
