Remark 62.11.8. Let $\Lambda _1 \to \Lambda _2$ be a homomorphism of torsion rings. Let $f : X \to Y$ be a separated finite type morphism of quasi-compact and quasi-separated schemes. The diagram

commutes where $res$ is the “restriction” functor which turns a $\Lambda _2$-module into a $\Lambda _1$-module using the given ring map. This holds by uniquenss of adjoints, the second commutative diagram of Remark 62.10.8 and because we have

This equality either for objects living over $X_{\acute{e}tale}$ or on $Y_{\acute{e}tale}$ is a very special case of Cohomology on Sites, Lemma 21.19.1.

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