Lemma 31.25.3 (01X5)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 31: Divisors
Section 31.25: Meromorphic functions and sections; reduced case
Lemma 31.25.3 (cite)

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

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