The Stacks project

Lemma 114.14.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $X = \bigcup _{j \in J} X_ j$ be a Zariski covering, see Spaces, Definition 64.12.5. If each $X_ j$ satisfies the sheaf property for the fpqc topology then $X$ satisfies the sheaf property for the fpqc topology.

Proof. This is true because all algebraic spaces satisfy the sheaf property for the fpqc topology, see Properties of Spaces, Proposition 65.17.1. $\square$

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