Lemma 47.24.6. Let $R \to R'$ be a homomorphism of Noetherian rings. Let $\varphi : R \to A$ be flat of finite type. Let $\varphi ' : R' \to A' = A \otimes _ R R'$ be the map induced by $\varphi $. Then we have a functorial isomorphism

for $K$ in $D(R)$.

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