The pure derived category of quasi-coherent sheaves. (English) Zbl 1440.14088
Summary: Let \(X\) be a quasi-compact and quasi-separated (not necessarily semi-separated) scheme. The category \(\mathfrak{Qco}X\) of all quasi-coherent sheaves of \(\mathcal{O}_X\)-modules has several different pure derived categories. Recently, categorical pure derived categories of \(X\) have been studied in more details. In this work, we focus on the geometrical purity and find a replacement for the geometrical pure derived category of \(X\).
MSC:
| 14F08 | Derived categories of sheaves, dg categories, and related constructions in algebraic geometry |
| 18G80 | Derived categories, triangulated categories |
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