Definition 71.7.6. Let S be a scheme. Let X be an algebraic space over S. Let \mathcal{L} be an invertible sheaf. Let s \in \Gamma (X, \mathcal{L}). The zero scheme of s is the closed subspace Z(s) \subset X defined by the quasi-coherent sheaf of ideals \mathcal{I} \subset \mathcal{O}_ X which is the image of the map s : \mathcal{L}^{\otimes -1} \to \mathcal{O}_ X.
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