Note on the Serre-Swan Theorem

Details Note on the Serre-Swan Theorem Note on the Serre-Swan Theorem

2009-05-04

arxiv.org/abs/0905.0319v1

Mathematics

Algebraic Geometry

8 pages; Accepted for publication in Mathematische Nachrichten

Scientific paper

We determine a class of ringed space X, for which the category of locally
free sheaves of bounded rank is equivalent to the category of finitely
generated projective A(X)-modules, where A(X) denote the ring of global
sections of X. The well-known Serre-Swan theorems for affine schemes,
differentiable manifolds, Stein spaces, etc., are then derived.

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