Proposition 26.20.6 (01KF): Valuative criterion of universal closedness

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Part 2: Schemes
Chapter 26: Schemes
Section 26.20: Valuative criterion for universal closedness
Proposition 26.20.6: Valuative criterion of universal closedness (cite)

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Proposition 26.20.6 (Valuative criterion of universal closedness). Let $f$ be a quasi-compact morphism of schemes. Then $f$ is universally closed if and only if $f$ satisfies the existence part of the valuative criterion.

Proof. This is a formal consequence of Lemmas 26.20.2 and 26.20.5 above. $\square$

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Comment #3813 by Kestutis Cesnavicius on November 28, 2018 at 07:33

Same comment as for https://stacks.math.columbia.edu/tag/01KE

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