A Lazard-like theorem for quasi-coherent sheaves

We study filtration of quasi–coherent sheaves. We prove a version of Kaplansky Theorem for quasi–coherent sheaves, by using Drinfeld’s notion of almost projective module and the Hill Lemma. We also show a Lazard-like theorem for flat quasi-coherent sheaves for quasi-compact and semi-separated schemes which satisfy the resolution property.