Lemma 27.11.7. With hypotheses and notation as in Lemma 27.11.1 above. Assume there exists a $g \in A_0$ such that $\psi$ induces an isomorphism $A_ g \to B$. Then $U(\psi ) = Y$, $r_\psi : Y \to X$ is an open immersion which induces an isomorphism of $Y$ with the inverse image of $D(g) \subset \mathop{\mathrm{Spec}}(A_0)$. Moreover the map $\theta$ is an isomorphism.

Proof. This is a special case of Lemma 27.11.6 above. $\square$

There are also:

• 2 comment(s) on Section 27.11: Functoriality of Proj

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).