Abstract
AbstractWe determine a class of ringed spaces,\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$(X,\mathcal {O}_{X})$\end{document}for which the category of locally free sheaves of bounded rank overXis equivalent to the category of finitely generated projective\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\Gamma ({X},{\mathcal {O}_{X}})$\end{document}‐modules. The well‐known Serre‐Swan theorems for affine schemes, differentiable manifolds, Stein spaces, etc., are then derived.
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