# ag.algebraic geometry – 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.