Lemma 28.26.12 (01Q2)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 28: Properties of Schemes
Section 28.26: Ample invertible sheaves
Lemma 28.26.12 (cite)

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Lemma 28.26.12. Let $X$ be a scheme. Let $S$ be a graded ring. Assume $X$ is quasi-compact, and assume there exists an open immersion

$j : X \longrightarrow Y = \text{Proj}(S).$

Then $j^*\mathcal{O}_ Y(d)$ is an invertible ample sheaf for some $d > 0$ .

Proof. This is Constructions, Lemma 27.10.6. $\square$

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