Lemma 31.25.3 (01X5)—The Stacks project

Processing math: 100%

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

previous lemma
next lemma

numberstags

history
statistics
1 tag refers to this tag

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. $\square$

Comments (0)

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).

Comments (0)

Post a comment