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Note on the Serre‐Swan theorem
Author(s) -
Morye Archana S.
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810263
Subject(s) - mathematics , rank (graph theory) , bounded function , affine transformation , class (philosophy) , pure mathematics , differentiable function , combinatorics , mathematical analysis , artificial intelligence , computer science
We 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 over X is 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.