Definition 87.24.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of locally Noetherian formal algebraic spaces over $S$. We say $f$ is a formal modification if

1. $f$ is a proper morphism (Formal Spaces, Definition 86.31.1),

2. $f$ is rig-étale,

3. $f$ is rig-surjective,

4. $\Delta _ f : X \to X \times _ Y X$ is rig-surjective.

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