Definition 67.48.3 (0822)—The Stacks project

Loading [MathJax]/extensions/tex2jax.js

Table of contents
Part 4: Algebraic Spaces
Chapter 67: Morphisms of Algebraic Spaces
Section 67.48: Relative normalization of algebraic spaces
Definition 67.48.3 (cite)

numberstags

Definition 67.48.3. Let $S$ be a scheme. Let $f : Y \to X$ be a quasi-compact and quasi-separated morphism of algebraic spaces over $S$. Let $\mathcal{O}'$ be the integral closure of $\mathcal{O}_ X$ in $f_*\mathcal{O}_ Y$. The normalization of $X$ in $Y$ is the morphism of algebraic spaces

\[ \nu : X' = \underline{\mathop{\mathrm{Spec}}}_ X(\mathcal{O}') \to X \]

over $S$. It comes equipped with a natural factorization

\[ Y \xrightarrow {f'} X' \xrightarrow {\nu } X \]

of the initial morphism $f$.

Comments (0)

There are also:

1 comment(s) on Section 67.48: Relative normalization of algebraic spaces

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