Lemma 15.95.10. Let $A$ be a ring and let $f \in A$ be a nonzerodivisor. Let $A \to B$ be a flat ring map and let $g \in B$ the image of $f$. Let $M^\bullet$ be a complex of $f$-torsion free $A$-modules. Then $g$ is a nonzerodivisor, $M^\bullet \otimes _ A B$ is a complex of $g$-torsion free modules, and $\eta _ fM^\bullet \otimes _ A B = \eta _ g(M^\bullet \otimes _ A B)$.

Proof. Omitted. $\square$

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