Definition 72.4.1 (0AD4)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 72: Algebraic Spaces over Fields
Section 72.4: Integral algebraic spaces
Definition 72.4.1 (cite)

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Definition 72.4.1. Let $S$ be a scheme. We say an algebraic space $X$ over $S$ is integral if it is reduced, decent, and $|X|$ is irreducible.

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