- 92-182 Bartocci C., Bruzzo U., Hernandez Ruiperez D., Pestov V.G.
- FOUNDATIONS OF SUPERMANIFOLD THEORY: THE AXIOMATIC APPROACH
(66K, AmSTeX -Requires style available from the second author)
Nov 10, 92
(auto. generated ps),
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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