Lemma 47.14.2. Let $R \to A$ and $R \to R'$ be ring maps and $A' = A \otimes _ R R'$. Assume

$A$ is pseudo-coherent as an $R$-module,

$R'$ has finite tor dimension as an $R$-module (for example $R \to R'$ is flat),

$A$ and $R'$ are tor independent over $R$.

Then (47.14.0.1) is an isomorphism for $K \in D^+(R)$.

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