Lemma 31.25.3. Let $X$ be an integral scheme with generic point $\eta$. We have

1. the sheaf of meromorphic functions is isomorphic to the constant sheaf with value the function field (see Morphisms, Definition 29.49.6) of $X$.

2. for any quasi-coherent sheaf $\mathcal{F}$ on $X$ the sheaf $\mathcal{K}_ X(\mathcal{F})$ is isomorphic to the constant sheaf with value $\mathcal{F}_\eta$.

Proof. Omitted. $\square$

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).