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- W4380136145 abstract "Let $(mathcal{G},otimes)$ be any closed symmetric monoidal Grothendieck category. We show that K-flat covers exist universally in the category of chain complexes and that the Verdier quotient of $K(mathcal{G})$ by the K-flat complexes is always a well generated triangulated category. Under the further assumption that $mathcal{G}$ has a set of $otimes$-flat generators we can show more: (i) The category is in recollement with the $otimes$-pure derived category and the usual derived category, and (ii) The usual derived category is the homotopy category of a cofibrantly generated and monoidal model structure whose cofibrant objects are precisely the K-flat complexes. We also give a condition guaranteeing that the right orthogonal to K-flat is precisely the acyclic complexes of $otimes$-pure injectives. We show this condition holds for quasi-coherent sheaves over a quasi-compact and semiseparated scheme." @default.
- W4380136145 created "2023-06-10" @default.
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- W4380136145 date "2023-06-07" @default.
- W4380136145 modified "2023-09-27" @default.
- W4380136145 title "K-flatness in Grothendieck categories: Application to quasi-coherent sheaves" @default.
- W4380136145 doi "https://doi.org/10.48550/arxiv.2306.04816" @default.
- W4380136145 hasPublicationYear "2023" @default.
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