Definition 28.26.1 (01PS)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 28: Properties of Schemes
Section 28.26: Ample invertible sheaves
Definition 28.26.1 (cite)

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[II Definition 4.5.3, EGA]

Definition 28.26.1. Let $X$ be a scheme. Let $\mathcal{L}$ be an invertible $\mathcal{O}_ X$ -module. We say $\mathcal{L}$ is ample if

$X$ is quasi-compact, and
for every $x \in X$ there exists an $n \geq 1$ and $s \in \Gamma (X, \mathcal{L}^{\otimes n})$ such that $x \in X_ s$ and $X_ s$ is affine.

Comments (2)

Comment #2689 by Matt Stevenson on August 01, 2017 at 23:13

This is EGA II Def 4.5.3

Comment #2716 by Takumi Murayama on August 01, 2017 at 23:39

Added reference; thanks!

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