The Stacks project

Remark 36.30.2. Let $R$ be a ring. Let $X$ be a scheme 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 36.30.1 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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