Note on the Serre-Swan theorem

Abstract

We determine a class of ringed spaces, (X, Ox) for which the category of locally free sheaves of bounded rank over X is equivalent to the category of finitely generated projective Γ(X, Ox-modules. The well-known Serre-Swan theorems for affine schemes, differentiable manifolds, Stein spaces, etc., are then derived. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.