The category of quasi-coherent sheaves on a non-affine scheme is well known not to have enough projectives. Neeman and Murfet have remedied this lack  by defining the derived category of flats as a suitable replacement of the homotopy category of projectives. This is so because a celebrated result by Neeman states that, in the affine case, the two categories are equivalent. But many concrete schemes satisfy the so-called resolution property, i.e. they have enough locally frees (so, in particular, enough infinite dimensional vector bundles in the sense of Drinfeld) so the class of infinite dimensional vector bundles constitutes a natural replacement of the flats in this case. In the talk we will show that, for such schemes, the derived category of flats is still triangulated equivalent to the derived category of vector bundles. The equivalence is indirect and strongly uses the class of very flat sheaves as recently defined by Positselski. The talk is based on a joint work with Alexander Slavick.