Lemma 56.16.4. If $A \to B$ is faithfully flat and $M$ is an $A$-module, then the complex $(B/A)_\bullet \otimes _ A M$ is exact in positive degrees, and $H^0((B/A)_\bullet \otimes _ A M) = M$.
Proof. See Descent, Lemma 34.3.6. $\square$
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