## The axioms of supermanifolds and a new structure arising from them

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- by Mitchell J. Rothstein PDF
- Trans. Amer. Math. Soc.
**297**(1986), 159-180 Request permission

## Abstract:

An analysis of supermanifolds over an arbitrary graded-commmutative algebra is given, proceeding from a set of axioms the first of which is that the derivations of the structure sheaf of a supermanifold are locally free. These axioms are satisfied not by the sheaf of ${G^\infty }$ functions, as has been asserted elsewhere, but by an extension of this sheaf. A given ${G^\infty }$ manifold may admit many supermanifold extensions, and it is unknown at present whether there are ${G^\infty }$ manifolds that admit no such extension. When the underlying graded-commutative algebra is commutative, the axioms reduce to the Berezin-Kostant supermanifold theory.## References

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## Additional Information

- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**297**(1986), 159-180 - MSC: Primary 58A50; Secondary 58C50
- DOI: https://doi.org/10.1090/S0002-9947-1986-0849473-8
- MathSciNet review: 849473