Lemma 15.73.13. Let $R$ be a ring. Let $a, b \in \mathbf{Z}$. Let $K^\bullet$ be a complex of $R$-modules. Let $R \to R'$ be a faithfully flat ring map. If the complex $K^\bullet \otimes _ R R'$ is perfect, then $K^\bullet$ is perfect.

Proof. Using Lemma 15.73.2 this translates into the corresponding results for pseudo-coherent modules and modules of finite tor dimension. See Lemma 15.65.17 and Lemma 15.63.15 for those results. $\square$

Comment #1689 by David Rydh on

This result should be about the descent of perfectness, not tor-amplitude (which is 068S). The proof is correct, but does not match the statement...

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