The Stacks project

Example 15.114.6. The equality in (6) of Lemma 15.114.5 is false without the assumption on $\kappa (\mathfrak m)$. A counterexample is the extension of $A = Z_2[t]_{(2)}$ given by $B = A[x]/(x^2 - t)$. Namely then $\sigma (x) = -x = x - 2x$ and $2x$ is not in $\mathfrak m^2$.

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View Example 15.114.6 as pdf