The Stacks project

Lemma 115.8.28. Let $f : X \to Y$ be a morphism of schemes which is locally quasi-finite. For an abelian group $A$ and a geometric point $\overline{y} : \mathop{\mathrm{Spec}}(k) \to Y$ we have $f^!(\overline{y}_*A) = \prod \nolimits _{f(\overline{x}) = \overline{y}} \overline{x}_*A$.

Proof. Follows from the corresponding statement in More Étale Cohomology, Lemma 63.6.1. $\square$

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