Remark 75.25.2 (0A1Q)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 75: Derived Categories of Spaces
Section 75.25: Cohomology and base change, VI
Remark 75.25.2 (cite)

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Remark 75.25.2. Let $R$ be a ring. Let $X$ be an algebraic space of finite presentation over $R$ . Let $\mathcal{G}$ be a finitely presented $\mathcal{O}_ X$ -module flat over $R$ with support proper over $R$ . By Lemma 75.25.1 there exists a finite complex of finite projective $R$ -modules $M^\bullet$ such that we have

$R\Gamma (X_{R'}, \mathcal{G}_{R'}) = M^\bullet \otimes _ R R'$

functorially in the $R$ -algebra $R'$ .

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