The Stacks project

Definition 75.9.1. Let $S$ be a scheme. A commutative diagram

of algebraic spaces over $S$ is called an elementary distinguished square if

1. $U$ is an open subspace of $W$ and $j$ is the inclusion morphism,

2. $f$ is étale, and

3. setting $T = W \setminus U$ (with reduced induced subspace structure) the morphism $f^{-1}(T) \to T$ is an isomorphism.

We will indicate this by saying: “Let $(U \subset W, f : V \to W)$ be an elementary distinguished square.”