… quasi-coherent sheaves have flat covers and cotorsion envelopes, we show that the pair (Cp(FlatX),
C(dg-CofX)) is a complete cotorsion theory … every flat complex of cotorsion modules …

… If every flat quasi-coherent sheaf has finite cotorsion … flat quasi-coherent sheaf has finite
pure injective dimension. Also, we show that there is an equivalence K(Pinf X) → Dpac(Flat X) of …

… to new and relevant questions on the class Flat ( X ) of flat quasi-coherent sheaves on X. For
instance, Murfet in [17, Remark B.7] raises the question of whether Flat ( X ) is closed under …

… quasi-coherent sheaves of O_X -modules. We show that any flat complex of cotorsion
quasi-coherent sheaves … the homotopy category of cotorsion flat quasi-coherent sheaves of O_X -…

… we prove the existence of a flat cover and a cotorsion envelope for any quasi-coherent …
proof of the existence of a flat cover for any quasi-coherent sheaf over the projective line . Some …

… of complexes of flat quasi-coherent sheaves, we show that all … countably presentable flat
quasi-coherent sheaves from the … , every flat quasi-coherent sheaf is a directed colimit of flat …

… flat cover and a cotorsion envelope for quasi-coherent R-modules. Then we use the fact that
the … of quasi-coherent sheaves on (X, OX) is equivalent to the category of quasi-coherent R-…

… cotorsion pair (very flat quasicoherent sheaves, contraadjusted … flat quasi-coherent sheaf
(or alternatively, a suitable direct sum of locally countably presented flat quasi-coherent sheaves…

… on Y relative to X and the derived category of X-flat pro-quasi-coherent pro-sheaves on Y
is constructed in Chap. 7. In particular, the semiderived category Dsi (-tors) itself is introduced …

… flat is precisely the acyclic complexes of \(\otimes\)-pure injectives. We show this condition
holds for quasi-coherent sheaves … but useful result concerning cotorsion pairs and direct limits (…