Lemma 53.2.1 (0BXY)—The Stacks project

Processing math: 100%

Table of contents
Part 3: Topics in Scheme Theory
Chapter 53: Algebraic Curves
Section 53.2: Curves and function fields
Lemma 53.2.1 (cite)

next lemma

numberstags

history
statistics
3 tags refer to this tag

Lemma 53.2.1. Let $k$ be a field. Let $X$ be a curve and $Y$ a proper variety. Let $U \subset X$ be a nonempty open and let $f : U \to Y$ be a morphism. If $x \in X$ is a closed point such that $\mathcal{O}_{X, x}$ is a discrete valuation ring, then there exist an open $U \subset U' \subset X$ containing $x$ and a morphism of varieties $f' : U' \to Y$ extending $f$ .

Proof. This is a special case of Morphisms, Lemma 29.42.5. $\square$

Comments (0)

There are also:

8 comment(s) on Section 53.2: Curves and function fields

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