The Stacks project

Lemma 38.43.5. In Situation 38.43.1 let $h : Y \to X$ be a morphism of schemes such that the pullback $E = h^{-1}D$ is defined. If $(X, D, M)$ is a good triple, then

\[ Lh^*(L\eta _\mathcal {I}M) = L\eta _\mathcal {J}(Lh^*M) \]

in $D(\mathcal{O}_ Y)$ where $\mathcal{J}$ is the ideal sheaf of $E$.

Proof. Translation of More on Algebra, Lemma 15.96.6. Use Lemmas 38.42.1 and 38.42.2 to do the translation. $\square$

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