Lemma 72.5.3 (0ENH)—The Stacks project

Processing math: 100%

Table of contents
Part 4: Algebraic Spaces
Chapter 72: Algebraic Spaces over Fields
Section 72.5: Morphisms between integral algebraic spaces
Lemma 72.5.3 (cite)

previous definition

numberstags

history
statistics
1 tag refers to this tag

Lemma 72.5.3. Let $S$ be a scheme. Let $X$ , $Y$ , $Z$ be integral algebraic spaces over $S$ . Let $f : X \to Y$ and $g : Y \to Z$ be dominant morphisms locally of finite type. Assume any of the equivalent conditions (1) – (5) of Lemma 72.5.1 hold for $f$ and $g$ . Then

$\deg (X/Z) = \deg (X/Y) \deg (Y/Z).$

Proof. This comes from the multiplicativity of degrees in towers of finite extensions of fields, see Fields, Lemma 9.7.7. $\square$

Comments (0)

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 toolbar).

Comments (0)

Post a comment