Remark on the Serre-Swan theorem for graded manifolds

Abstract: Combining the Batchelor theorem and the Serre-Swan theorem, we come to that, given a smooth manifold

X

, a graded commutative

C^{i} n f t y (X)

-algebra

c A

is isomorphic to the structure ring of a graded manifold with a body

X

iff it is the exterior algebra of some projective

C^{i} n f t y (X)

-module of finite rank. In particular, it follows that odd fields in field theory on a smooth manifold

X

can be represented by graded functions on some graded manifold with body

X

.

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