Note on the Serre‐Swan theorem
Copyright policy )Note on the Serre‐Swan theorem
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.
16D40, 18F20 (Secondary), projective modules, Serre-Swan theorem, Free, projective, and flat modules and ideals in associative algebras, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Sheaves, derived categories of sheaves, etc., vector bundles, Mathematics - Algebraic Geometry, 14F05 (Primary); 16D40, 18F20 (Secondary), FOS: Mathematics, 14F05 (Primary), Algebraic Geometry (math.AG)
16D40, 18F20 (Secondary), projective modules, Serre-Swan theorem, Free, projective, and flat modules and ideals in associative algebras, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Sheaves, derived categories of sheaves, etc., vector bundles, Mathematics - Algebraic Geometry, 14F05 (Primary); 16D40, 18F20 (Secondary), FOS: Mathematics, 14F05 (Primary), Algebraic Geometry (math.AG)
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