diff --git a/more-algebra.tex b/more-algebra.tex index 821e9aba..2492d79e 100644 --- a/more-algebra.tex +++ b/more-algebra.tex @@ -6196,7 +6196,7 @@ \section{Completion and flatness} as $M_n$ is flat over $A/I^n$. By Lemma \ref{lemma-tor-strictly-pro-zero} we see that this system is essentially constant (with value $0$). It follows from Homology, Lemma \ref{homology-lemma-apply-Mittag-Leffler-again} -that $\lim Q \otimes_A A/I^n = +that $\lim Q \otimes_A M_n = \Coker(\lim F_1 \otimes_A M_n \to \lim F_0 \otimes_A M_n)$. Since $F_i$ is finite free this equals $\Coker(F_1 \otimes_A M \to F_0 \otimes_A M) = Q \otimes_A M$.