Lemma 37.40.2. Let f : U \to S be a surjective étale morphism of affine schemes. There exists a surjective, finite locally free morphism \pi : T \to S and a finite open covering T = T_1 \cup \ldots \cup T_ n such that each T_ i \to S factors through U \to S. Diagram:
\xymatrix{ & \coprod T_ i \ar[rd] \ar[ld] & \\ T \ar[rd]^\pi & & U \ar[ld]_ f \\ & S & }
where the south-west arrow is a Zariski-covering.
Comments (0)