Lemma 29.54.10 (035R)—The Stacks project

Processing math: 100%

Table of contents
Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.54: Normalization
Lemma 29.54.10 (cite)

previous lemma
next lemma

numberstags

history
statistics
1 tag refers to this tag

Lemma 29.54.10. Let $X$ be an integral, Japanese scheme. The normalization $\nu : X^\nu \to X$ is a finite morphism.

Proof. Follows from the definition (Properties, Definition 28.13.1) and Lemma 29.54.3. Namely, in this case the lemma says that $\nu ^{-1}(\mathop{\mathrm{Spec}}(A))$ is the spectrum of the integral closure of $A$ in its field of fractions. $\square$

Comments (0)

There are also:

2 comment(s) on Section 29.54: Normalization

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