Separated morphism

Summary

A separated morphism $X \to Y$ is a morphism of schemes whose diagonal $X \to X \times_Y X$ is a closed immersion. It is the scheme version of the Hausdorff property, which fails for the Zariski topology itself. A scheme is separated if its morphism to $\operatorname{Spec} \Z$ is separated; all affine and all projective schemes are separated.