From 04b36aa01973d0a5f9e86250e5666d0d11690c4c Mon Sep 17 00:00:00 2001 From: Aise Johan de Jong Date: Sat, 13 Apr 2024 13:52:56 -0400 Subject: [PATCH] Two typos in etale-cohomology Thanks to Niels and Alexander Schmidt https://stacks.math.columbia.edu/tag/0EYQ#comment-8363 https://stacks.math.columbia.edu/tag/0EYQ#comment-8820 --- etale-cohomology.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/etale-cohomology.tex b/etale-cohomology.tex index dd5183f5..cbccc382 100644 --- a/etale-cohomology.tex +++ b/etale-cohomology.tex @@ -17319,7 +17319,7 @@ \section{Smooth base change} Assume $q = 1$. Recall that $\mathcal{F}$ corresponds to a discrete module $M$ with continuous $\text{Gal}_K$-action, see Lemma \ref{lemma-equivalence-abelian-sheaves-point}. -Since $M$ is $n$-torsion, it is the uninon of finite +Since $M$ is $n$-torsion, it is the union of finite $\text{Gal}_K$-stable subgroups. Thus we reduce to the case where $M$ is a finite abelian group annihilated by $n$, see Lemma \ref{lemma-colimit}. After replacing $K$ by a finite extension @@ -17902,7 +17902,7 @@ \section{Smooth base change} \end{proof} \noindent -The following immediate consquence of the smooth base change +The following immediate consequence of the smooth base change theorem is what is often used in practice. \begin{lemma}