The Stacks project

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

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

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

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

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

Proof. Follows from Lemma 47.14.1 and More on Algebra, Lemma 15.98.3 part (4). $\square$

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