Pure exact structures and the pure derived category of a scheme

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 $\mathbf{C}(\mathcal{C})$ of unbounded chain complexes in $\mathcal{C}$. We use $\lambda$-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.

References in corpus (1)

• The derived category with respect to a generator

Cited by in corpus (1)

• Pure resolutions of unbounded complexes of modules