The Stacks project

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. $\square$

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