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

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

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

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