Lemma 36.33.1 (0EX6)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 36: Derived Categories of Schemes
Section 36.33: Other applications
Lemma 36.33.1 (cite)

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Lemma 36.33.1. Let $R$ be a coherent ring. Let $X$ be a scheme of finite presentation over $R$. Let $\mathcal{G}$ be an $\mathcal{O}_ X$-module of finite presentation, flat over $R$, with support proper over $R$. Then $H^ i(X, \mathcal{G})$ is a coherent $R$-module.

Proof. Combine Lemma 36.30.1 with More on Algebra, Lemmas 15.64.18 and 15.74.2. $\square$

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