Let $X$ be a quasicompact quasiseparated scheme. Consider the full subcategory $\text{Qcoh}_{fp}(X)$ of $\text{Qcoh}(X)$ which consists of the quasi-coherent modules which are locally of finite presentation.

**Question** Is every quasi-coherent module $M$ the colimit of the homomorphisms $N \to M$, where $N$ runs through $\text{Qcoh}_{fp}(X)$?

Note that this makes sense since $\text{Qcoh}_{fp}(X)$ is essentially small. The result is well-known if we allow quasi-coherent modules which are of finite type (in particular, everything is OK if $X$ is noetherian). If $X$ is affine, then the result is trivial.