# The Stacks Project

## Tag 03HV

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 4336–4341 (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}

There are no comments yet for this tag.

There are also 2 comments on Section 28.24: Morphisms of Schemes.

## Add a comment on tag 03HV

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the lower-right corner).