Lemma 18.40.3 (05D8)—The Stacks project

Processing math: 100%

Table of contents
Part 1: Preliminaries
Chapter 18: Modules on Sites
Section 18.40: Locally ringed topoi
Lemma 18.40.3 (cite)

previous lemma
next definition

numberstags

history
statistics
2 tags refer to this tag

Lemma 18.40.3. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Consider the statements

(18.40.2.1) is an isomorphism, and
for every point $p$ of $\mathcal{C}$ the stalk $\mathcal{O}_ p$ is not the zero ring.

We always have (1) $\Rightarrow$ (2) and if $\mathcal{C}$ has enough points then (1) $\Leftrightarrow$ (2).

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