Abstract
Let [Formula: see text] be a quasi-compact and semi-separated scheme. If every flat quasi-coherent sheaf has finite cotorsion dimension, we prove that [Formula: see text] is [Formula: see text]-perfect for some [Formula: see text]. If [Formula: see text] is coherent and [Formula: see text]-perfect (not necessarily of finite Krull dimension), we prove that every flat quasi-coherent sheaf has finite pure injective dimension. Also, we show that there is an equivalence [Formula: see text] of homotopy categories, whenever [Formula: see text] is the homotopy category of pure injective flat quasi-coherent sheaves and [Formula: see text] is the pure derived category of flat quasi-coherent sheaves.
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