Lemma 29.57.5 (03J7)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.57: Universally bounded fibres
Lemma 29.57.5 (cite)

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Lemma 29.57.5. A base change of a morphism with universally bounded fibres is a morphism with universally bounded fibres. More precisely, if $n$ bounds the degrees of the fibres of $f : X \to Y$ and $Y' \to Y$ is any morphism, then the degrees of the fibres of the base change $f' : Y' \times _ Y X \to Y'$ is also bounded by $n$.

Proof. This is clear from the result of Lemma 29.57.2. $\square$

Comments (2)

Comment #2347 by Eric Ahlqvist on January 11, 2017 at 08:48

There is one " $\to Y'$ " too many in the end of the lemma.

Comment #2416 by Johan on February 17, 2017 at 13:49

Thanks. Fixed here.

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