# Is Qcoh(X) locally presentable?

Let $$X$$ be a scheme. Is the category $$QCoh(X)$$ of quasi-coherent sheaves on $$X$$ locally presentable? If so, can we say anything about the $$\kappa$$ for which $$QCoh(X)$$ is locally $$\kappa$$-presentable? (e.g. is it always finitely presentable? Or related to the $$\kappa$$ of Gabber's result?)

I'm particularly interested in the case where $$X$$ is quasi-comact quasi-separated (qcqs).

In my searching for references, I've come across answers ranging from "we don't know", "when qcqs", to "always", and would appreciate some clarity.

$$\operatorname{QCoh}(X)=\lim_{U\subseteq X} \operatorname{QCoh}(U)$$
where $$U$$ ranges through all open affines and the limit is taken in the $$(2,1)$$-categorical sense. Since small limits of presentable categories are presentable and $$\operatorname{QCoh}(\operatorname{Spec}R)=\operatorname{Mod}_R$$ is presentable, we have that that $$\operatorname{QCoh}(X)$$ is presentable.
I'm not sure how to get bounds on the accessibility degree in general, though when $$X$$ is qcqs it is compactly generated (i.e. $$\omega$$-presentable) by the argument in this answer by Denis-Charles Cisinski.