From 5c8d8cc9203fe7137a33824b2949bf190776fa90 Mon Sep 17 00:00:00 2001 From: Aise Johan de Jong Date: Mon, 22 Oct 2018 17:25:41 -0400 Subject: [PATCH] X \to Y should be Y \to X (2x) THanks to Neeraj Deshmukh https://stacks.math.columbia.edu/tag/0271#comment-3580 --- examples.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/examples.tex b/examples.tex index 078778353..665876b36 100644 --- a/examples.tex +++ b/examples.tex @@ -1475,9 +1475,9 @@ \section{Non-quasi-affine variety with quasi-affine normalization} ring map $A \otimes_k B \to B_{x + y}$ is surjective. To see this use that $A \otimes_k B$ contains the element $xy/(x + y) \otimes 1/xy$ which maps to $1/(x + y)$. -The morphism $X \to Y$ is given by the natural maps +The morphism $Y \to X$ is given by the natural maps $D(x + y) \to \Spec(A)$ and $D(xy) \to \Spec(B)$. -Since these are both finite we deduce that $X \to Y$ is finite +Since these are both finite we deduce that $Y \to X$ is finite as desired. We omit the verification that $X$ is indeed the coequalizer of the displayed diagram above, however, see (insert future reference for pushouts in the category of schemes