Lemma 54.70.8. Let $X$ be a quasi-compact and quasi-separated scheme.

Let $\mathcal{F} \to \mathcal{G}$ be a map of constructible sheaves of sets on $X_{\acute{e}tale}$. Then the set of points $x \in X$ where $\mathcal{F}_{\overline{x}} \to \mathcal{G}_{\overline{x}}$ is surjective, resp. injective, resp. is isomorphic to a given map of sets, is constructible in $X$.

Let $\mathcal{F}$ be a constructible abelian sheaf on $X_{\acute{e}tale}$. The support of $\mathcal{F}$ is constructible.

Let $\Lambda $ be a Noetherian ring. Let $\mathcal{F}$ be a constructible sheaf of $\Lambda $-modules on $X_{\acute{e}tale}$. The support of $\mathcal{F}$ is constructible.

## Comments (3)

Comment #2357 by Simon Pepin Lehalleur on

Comment #3387 by Dario on

Comment #3609 by Ayush on

There are also: