Lemma 20.21.2. Let $i : Z \to X$ be the inclusion of a closed subset. Let $\mathcal{G}$ be an injective abelian sheaf on $Z$. Then $\mathcal{H}^ p_ Z(i_*\mathcal{G}) = 0$ for $p > 0$.

**Proof.**
This is true because the functor $i_*$ is exact and transforms injective abelian sheaves into injective abelian sheaves by Lemma 20.11.11.
$\square$

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