The completeness conjecture for quasi-compact and quasi-separated algebraic stacks

Let $X$ be a quasi-compact and quasi-separated algebraic stack. A quasi-coherent $\mathcal{O}_X$-module is said to have the completeness property when it is a directed colimit of finitely presented $\mathcal{O}_X$-modules. Completeness conjecture. If $X$ is a quasi-compact and quasi-separated algebraic stack, then $X$ has the completeness property. The partial completeness property is known in this generality: every quasi-coherent module is a union of its quasi-coherent submodules of finite type. The conjecture asks for the stronger finitely presented filtration statement, which is known for schemes, algebraic spaces, and Deligne–Mumford stacks but remains open for general algebraic stacks with infinite stabilizers.