# ag.algebraic geometry – Is Qcoh(X) domestically presentable? Answer

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ag.algebraic geometry – Is Qcoh(X) domestically presentable?

Let $$X$$ breathe a strategy. Is the class $$QCoh(X)$$ of quasi-coherent sheaves on $$X$$ domestically presentable? If so, can we are saying something in regards to the $$kappa$$ for which $$QCoh(X)$$ is domestically $$kappa$$-presentable? (e.g. is it at all times finitely presentable? Or associated to the $$kappa$$ of Gabber’s outcome?)

I’m notably within the illustration the place $$X$$ is quasi-comact quasi-separated (qcqs).

In my trying to find references, I’ve come throughout solutions starting from “we don’t know”, “when qcqs”, to “always”, and would value some readability.

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