Definition 72.8.1 (0AD8)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 72: Algebraic Spaces over Fields
Section 72.8: Modifications and alterations
Definition 72.8.1 (cite)

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Definition 72.8.1. Let $S$ be a scheme. Let $X$ be an integral algebraic space over $S$ . A modification of $X$ is a birational proper morphism $f : X' \to X$ of algebraic spaces over $S$ with $X'$ integral.

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