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The Serre-Swan Theorem for Ringed Spaces

In: Analytic and Algebraic Geometry

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  • Archana S. Morye

    (University of Hyderabad, School of Mathematics and Statistics)

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.

Suggested Citation

  • Archana S. Morye, 2017. "The Serre-Swan Theorem for Ringed Spaces," Springer Books, in: Anilatmaja Aryasomayajula & Indranil Biswas & Archana S. Morye & A. J. Parameswaran (ed.), Analytic and Algebraic Geometry, pages 207-223, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-5648-2_13
    DOI: 10.1007/978-981-10-5648-2_13
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