Definition 65.20.3. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\mathcal{F}$ be an abelian sheaf on $X_{\acute{e}tale}$.

The

*support of $\mathcal{F}$*is the set of points $x \in |X|$ such that $\mathcal{F}_{\overline{x}} \not= 0$ for any (some) geometric point $\overline{x}$ lying over $x$.Let $\sigma \in \mathcal{F}(U)$ be a section. The

*support of $\sigma $*is the closed subset $U \setminus W$, where $W \subset U$ is the largest open subset of $U$ on which $\sigma $ restricts to zero (see Lemma 65.20.2).

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