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- Jun 20, 2014

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Suppose $(X, \mathscr{O}_X)$ is a locally ringed space. Show that for all $\mathscr{O}_X$-modules $\mathscr{F}$ and $\mathscr{G}$ of finite type, $\operatorname{Supp}(\mathscr{F}\otimes_{\mathscr{O}_X} \mathscr{G}) = \operatorname{Supp}(\mathscr{F})\cap \operatorname{Supp}(\mathscr{G})$.

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