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

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

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.
$\square$

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like `$\pi$`

). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)