  Let X be e quasi-compact and semi-separated scheme. If every at quasi-
coherent sheaf has finite cotorsion dimension, we prove that X is n-perfect for
some n > 0. If X is coherent and n-perfect(not necessarily of finite krull
dimension), we prove that every at quasi-coherent sheaf has finite pure
injective dimension. Also, we show that there is an equivalence K(PinfX)--->
D(FlatX) of homotopy categories, whenever K(PinfX) is the homotopy category of
pure injective at quasi-coherent sheaves and D(FlatX) is the pure derived
category of at quasi-coherent sheaves.
