Lemma 29.37.6 (0891)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.37: Relatively ample sheaves
Lemma 29.37.6 (cite)

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[II Proposition 5.1.6, EGA]

Lemma 29.37.6. Let $f : X \to S$ be a morphism of schemes. Then $f$ is quasi-affine if and only if $\mathcal{O}_ X$ is $f$ -relatively ample.

Proof. Follows from Properties, Lemma 28.27.1 and the definitions. $\square$

Comments (2)

Comment #2708 by Matt Stevenson on August 01, 2017 at 23:31

This is closely related to EGA II Prop 5.1.6 (it is the equivalence of (a) and (c'), but in EGA the morphism f is assumed to be quasi-compact).

Comment #2745 by Takumi Murayama on August 02, 2017 at 00:07

Added reference; thanks!

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