\begin{align*} \Theta_K : G_K^{\operatorname{ab}}\xrightarrow{\sim} \widehat{K^^{\times}} .\end{align*}
where \(\widehat{{-}}\) denotes the profinite completion.
\begin{align*} \Theta_K : G_K^{\operatorname{ab}}\xrightarrow{\sim} \widehat{K^^{\times}} .\end{align*}
where \(\widehat{{-}}\) denotes the profinite completion.