The Stacks project

Definition 59.27.1. An étale covering of a scheme $U$ is a family of morphisms of schemes $\{ \varphi _ i : U_ i \to U\} _{i \in I}$ such that

1. each $\varphi _ i$ is an étale morphism,

2. the $U_ i$ cover $U$, i.e., $U = \bigcup _{i\in I}\varphi _ i(U_ i)$.