Indexed on: 13 May '16Published on: 11 Jan '16Published in: Journal of Algebra and Its Applications
Journal of Algebra and Its Applications, Ahead of Print. Let [math] be a quasi-compact and semi-separated scheme. If every flat quasi-coherent sheaf has finite cotorsion dimension, we prove that [math] is [math]-perfect for some [math]. If [math] is coherent and [math]-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 [math] of homotopy categories, whenever [math] is the homotopy category of pure injective flat quasi-coherent sheaves and [math] is the pure derived category of flat quasi-coherent sheaves.