Note on the Serre-Swan Theorem

2009/05/04 by Archana S. Morye, Morye, Archana S. · 1 citation
Mathematics · #14F05 (Primary) #16D40 #18F20 (Secondary) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14F05 #msc:16D40 #msc:18F20

paper · pdf · doi:10.48550/arxiv.0905.0319

8 pages; Accepted for publication in Mathematische Nachrichten

arxiv created 2009/05/04 · openalex publication_date 2009/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine a class of ringed space X, for which the category of locally free sheaves of bounded rank is equivalent to the category of finitely generated projective A(X)-modules, where A(X) denote the ring of global sections of X. The well-known Serre-Swan theorems for affine schemes, differentiable manifolds, Stein spaces, etc., are then derived.

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