Lemma 29.14.8. The following properties of ring maps are stable under base change.

(Isomorphism on local rings.) For every prime $\mathfrak q$ of $A$ lying over $\mathfrak p \subset R$ the ring map $R \to A$ induces an isomorphism $R_{\mathfrak p} \to A_{\mathfrak q}$.

(Open immersion.) For every prime $\mathfrak q$ of $A$ there exists an $f \in R$, $\varphi (f) \not\in \mathfrak q$ such that the ring map $\varphi : R \to A$ induces an isomorphism $R_ f \to A_ f$.

Add more here as needed

^{1}.

## Comments (2)

Comment #2246 by JuanPablo on

Comment #2281 by Johan on