Lemma 17.9.6. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{F}$ be a sheaf of $\mathcal{O}_ X$-modules. If $\mathcal{F}$ is of finite type then support of $\mathcal{F}$ is closed.

** Over any ringed space, sheaves of modules of finite type have closed support. **

**Proof.**
This is a reformulation of Lemma 17.9.5.
$\square$

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## Comments (1)

Comment #889 by Konrad Voelkel on

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