Lemma 76.7.4. Let S be a scheme. Let f : X \to Y be a morphism of algebraic spaces over S. Then \Omega _{X/Y} is a quasi-coherent \mathcal{O}_ X-module.
Proof. Choose a diagram as in Lemma 76.7.3 with a and b surjective and U and V schemes. Then we see that \Omega _{X/Y}|_ U = \Omega _{U/V} which is quasi-coherent (for example by Morphisms, Lemma 29.32.7). Hence we conclude that \Omega _{X/Y} is quasi-coherent by Properties of Spaces, Lemma 66.29.6. \square
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