The Serre-Swan Theorem for Ringed Spaces

Archana S. Morye ()
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Archana S. Morye: University of Hyderabad, School of Mathematics and Statistics

A chapter in Analytic and Algebraic Geometry, 2017, pp 207-223 from Springer

Abstract: Abstract In this article we prove that if every locally free sheaf of bounded rank over aringed space X is acyclic and generated by finitely many global sections, then the category of locally free sheaves of bounded rank over X is equivalent tothe category of finitely generated projective modules over the ring of its global sections. This result is a generalization of the classical results of Serre for affine schemes, and of Swan for paracompact topological spaces.

Keywords: Serre-Swan Theorem; vector bundles; projective modules (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-5648-2_13

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DOI: 10.1007/978-981-10-5648-2_13

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