Lemma 18.24.1 (082T)—The Stacks project

Processing math: 100%

Table of contents
Part 1: Preliminaries
Chapter 18: Modules on Sites
Section 18.24: Basic results on local types of modules
Lemma 18.24.1 (cite)

next lemma

numberstags

history
statistics
6 tags refer to this tag

Lemma 18.24.1. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\theta : \mathcal{G} \to \mathcal{F}$ be a surjective $\mathcal{O}$ -module map with $\mathcal{F}$ of finite presentation and $\mathcal{G}$ of finite type. Then $\mathop{\mathrm{Ker}}(\theta )$ is of finite type.

Proof. Omitted. Hint: See Modules, Lemma 17.11.3. $\square$

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