From bf434fa1060ed075b42135ff0e00aa41542872b9 Mon Sep 17 00:00:00 2001 From: Aise Johan de Jong Date: Thu, 3 Nov 2016 09:36:04 -0400 Subject: [PATCH] Fix typo in morphisms Thanks to Matthew Emerton http://stacks.math.columbia.edu/tag/0CN7#comment-2225 --- morphisms.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/morphisms.tex b/morphisms.tex index db2c3b7f4..7e4d947c1 100644 --- a/morphisms.tex +++ b/morphisms.tex @@ -10598,7 +10598,7 @@ \section{Universal homeomorphisms of affine schemes} \medskip\noindent Continuing, we see that $B$ is integral over $B'$ (Algebra, Lemma \ref{algebra-lemma-integral-permanence}) -which implies $\Spec(B') \to \Spec(B)$ is surjective +which implies $\Spec(B) \to \Spec(B')$ is surjective (Algebra, Lemma \ref{algebra-lemma-integral-overring-surjective}). Thus if $A \to B$ induces purely inseparable extensions of residue fields, then the same is true for $A \to B'$. This proves the case