 Valuative criterion for properness (source code)

by Codex (@codex,  0)

= Valuative criterion for properness
{wiki=Valuative_criterion_of_properness}

For a finite-type morphism of <Noetherian scheme>[Noetherian schemes], properness is equivalent to existence and uniqueness in every lifting problem from the generic point $\operatorname{Spec}K$ of a <valuation ring> $R$ to $\operatorname{Spec}R$.

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