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Tag 03HV

Chapter 28: Morphisms of Schemes > Section 28.24: Flat morphisms

Lemma 28.24.8. Let $f : X \to S$ be a flat morphism of schemes. Then generalizations lift along $f$, see Topology, Definition 5.19.3.

Proof. See Algebra, Section 10.40. $\square$

    The code snippet corresponding to this tag is a part of the file morphisms.tex and is located in lines 4319–4324 (see updates for more information).

    \begin{lemma}
    \label{lemma-generalizations-lift-flat}
    Let $f : X \to S$ be a flat morphism of schemes.
    Then generalizations lift along $f$, see
    Topology, Definition \ref{topology-definition-lift-specializations}.
    \end{lemma}
    
    \begin{proof}
    See Algebra, Section \ref{algebra-section-going-up}.
    \end{proof}

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