The homotopy category of acyclic complexes of pure-projective modules

James Gillespie

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arXiv · 2201.05542

The homotopy category of acyclic complexes of pure-projective modules

James Gillespie

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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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James Gillespie. 2022-01-14. The homotopy category of acyclic complexes of pure-projective modules. https://arxiv.org/abs/2201.05542

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