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Proper base change for étale cohomology holds for finite morphisms.

Lemma 59.91.9. Let $f : X \to Y$ be a finite morphism of schemes. Then cohomology commutes with base change for $f$.

Proof. Observe that a finite morphism is proper, see Morphisms, Lemma 29.44.11. Moreover, the base change of a finite morphism is finite, see Morphisms, Lemma 29.44.6. Thus the result follows from Lemma 59.91.6 combined with Proposition 59.55.2. $\square$

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Comment #986 by on

Suggested slogan: Etale cohomology commutes with finite base change.

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  • 4 comment(s) on Section 59.91: The proper base change theorem

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