Lemma 35.37.2. Let S be a scheme. Let \{ X_ i \to S\} _{i\in I} be an fpqc covering, see Topologies, Definition 34.9.1. Let (V_ i/X_ i, \varphi _{ij}) be a descent datum relative to \{ X_ i \to S\} . If each morphism V_ i \to X_ i is a closed immersion, then the descent datum is effective.
Proof. This is true because a closed immersion is an affine morphism (Morphisms, Lemma 29.11.9), and hence Lemma 35.37.1 applies. \square
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