Lemma 17.16.2. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{F}'$, $\mathcal{G}'$ be presheaves of $\mathcal{O}_ X$-modules with sheafifications $\mathcal{F}$, $\mathcal{G}$. Then $\mathcal{F} \otimes _{\mathcal{O}_ X} \mathcal{G} = (\mathcal{F}' \otimes _{p, \mathcal{O}_ X} \mathcal{G}')^\#$.

Proof. Omitted. $\square$

There are also:

• 5 comment(s) on Section 17.16: Tensor product

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).