Remark 62.3.9 (Open embeddings and compactly supported sections). Let $X$ be a separated scheme locally of finite type over a field $k$. Let $\mathcal{F}$ be an abelian sheaf on $X_{\acute{e}tale}$. Exactly as in Remark 62.3.5 for $X' \subset X$ open there is an injective map

and these maps turn $H^0_ c$ into a “cosheaf” on the Zariski site of $X$.

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