Lemma 48.12.4. Let g : Y' \to Y be a morphism of quasi-compact and quasi-separated schemes. Let f : X \to Y be a proper, flat morphism of finite presentation. Then the base change map (48.5.0.1) is an isomorphism for all K \in D_\mathit{QCoh}(\mathcal{O}_ Y).
Proof. By Lemma 48.12.2 formation of the functors a and a' commutes with restriction to opens of Y and Y'. Hence we may assume Y' \to Y is a morphism of affine schemes, see Remark 48.6.1. In this case the statement follows from Lemma 48.6.2. \square
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