Lemma 85.28.3. Let $f : V \to U$ be a cartesian morphism of simplicial schemes. Assume the morphisms $d^ n_ j : U_ n \to U_{n - 1}$ are flat and the morphisms $V_ n \to U_ n$ are quasi-compact and quasi-separated. Then $f^*$ and $f_*$ form an adjoint pair of functors between the categories of quasi-coherent modules on $U_{Zar}$ and $V_{Zar}$.
Proof. We have seen in Lemmas 85.28.1 and 85.28.2 that the statement makes sense. The adjointness property follows immediately from the fact that each $f_ n^*$ is adjoint to $f_{n, *}$. $\square$
Post a comment
Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)