42.5.4.1
\begin{equation} \label{chow-equation-to-prove} \left(\text{Norm}_{\kappa _ j/\kappa }(u \bmod \mathfrak m_ j)^{m_ j}\right)^ m = \prod \nolimits _ l \text{Norm}_{\kappa '_{j, l}/\kappa '}(u \bmod \mathfrak m'_{j, l})^{m'_{j, l}} \end{equation}
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