The Stacks project

[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

  1. $X$ is quasi-compact, and

  2. 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

This is EGA II Def 4.5.3

There are also:

  • 5 comment(s) on Section 28.26: Ample invertible sheaves

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View Definition 28.26.1 as pdf