Definition 7.6.
A morphism \((f,f^{\sharp})\colon (T,\Oo_T) \to (S,\Oo_S)\) of Zariski schemes is called étale if the underlying morphism of topoi \(f\) is étale and the adjoint structural morphism
\[f^*\Oo_S \longrightarrow \Oo_T\]
is an isomorphism. This use of the word étale is unrelated to the notion of an étale scheme from Definition 7.3. For example, every morphism which is locally on source and target an open immersion of schemes is étale in this sense.