Lemma 28.27.2 (0BCK)—The Stacks project

Processing math: 100%

Table of contents
Part 2: Schemes
Chapter 28: Properties of Schemes
Section 28.27: Affine and quasi-affine schemes
Lemma 28.27.2 (cite)

previous lemma
next lemma

numberstags

history
statistics
1 tag refers to this tag

Lemma 28.27.2. Let $X$ be a quasi-affine scheme. For any quasi-compact immersion $i : X' \to X$ the scheme $X'$ is quasi-affine.

Proof. This can be proved directly without making use of the material on ample invertible sheaves; we urge the reader to do this on a napkin. Since $X$ is quasi-affine, we have that $\mathcal{O}_ X$ is ample by Lemma 28.27.1. Then $\mathcal{O}_{X'}$ is ample by Lemma 28.26.14. Then $X'$ is quasi-affine by Lemma 28.27.1. $\square$

Comments (0)

There are also:

2 comment(s) on Section 28.27: Affine and quasi-affine schemes

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