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The homotopy category of acyclic complexes of pure-projective modules

2022/01/14 by James Gillespie, Gillespie, James
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2201.05542

Abstract

Let R be any ring with identity. We show that the homotopy category of all acyclic chain complexes of pure-projective R-modules is a compactly generated triangulated category. We do this by constructing abelian model structures that put this homotopy category into a recollement with two other compactly generated triangulated categories: The usual derived category of R and the pure derived category of R. This also gives a new model for the derived category.

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