Definition 73.9.1. Let $S$ be a scheme. A commutative diagram

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

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

$f$ is étale, and

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.”

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