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Tag 0CLL

Chapter 91: Morphisms of Algebraic Stacks > Section 91.38: Valuative criteria

Lemma 91.38.11. The base change of a morphism of algebraic stacks which satisfies the existence part of the valuative criterion by any morphism of algebraic stacks is a morphism of algebraic stacks which satisfies the existence part of the valuative criterion.

Proof. Follows from Lemma 91.38.4 and the definition. $\square$

    The code snippet corresponding to this tag is a part of the file stacks-morphisms.tex and is located in lines 8907–8913 (see updates for more information).

    \begin{lemma}
    \label{lemma-base-change-existence}
    The base change of a morphism of algebraic stacks which satisfies the
    existence part of the valuative criterion by any morphism of
    algebraic stacks is a morphism of algebraic stacks which satisfies the
    existence part of the valuative criterion.
    \end{lemma}
    
    \begin{proof}
    Follows from Lemma \ref{lemma-cat-dotted-arrows-base-change}
    and the definition.
    \end{proof}

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