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The Stacks project

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

\[ \xymatrix{ U \times _ W V \ar[r] \ar[d] & V \ar[d]^ f \\ U \ar[r]^ j & W } \]

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.”

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View Definition 75.9.1 as pdf