Pure exact structures and the pure derived category of a scheme

2014/08/12 by Sergio Estrada, James Gillespie, Estrada, Sergio +3 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1408.2846

openalex publication_date 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathcal C be closed symmetric monoidal Grothendieck category. We define the pure derived category with respect to the monoidal structure via a relative injective model category structure on the category C(\mathcal C) of unbounded chain complexes in \mathcal C. We use λ-Purity techniques to get this. As application we define the stalkwise pure derived category of the category of quasi--coherent sheaves on a quasi-separated scheme. We also give a different approach by using the category of flat quasi--coherent sheaves.

Citations

• The derived category with respect to a generator

Cited by

• Kaplansky classes and stability
• On Pure Derived Categories

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