Lemma 70.10.5. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Assume

every weakly associated point of $X$ is a point of codimension $0$, and

$X$ satisfies the equivalent conditions of Morphisms of Spaces, Lemma 66.49.1.

$X$ is representable by a scheme $X_0$ (awkward but temporary notation).

Then the sheaf of meromorphic functions $\mathcal{K}_ X$ is the quasi-coherent sheaf of $\mathcal{O}_ X$-algebras associated to the quasi-coherent sheaf of meromorphic functions $\mathcal{K}_{X_0}$.

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