= Lubin–Tate tower
{c}
{title2=$K_\pi=\bigcup_{n\geq1}K_{\pi,n}$}
Choose compatible primitive <Lubin–Tate torsion> points with $[\pi]\lambda_{n+1}=\lambda_n$. Restriction of the <Lubin–Tate Galois action on primitive torsion> is reduction of <unit> classes modulo $\pi^n$. The <inverse limit> gives
$$
\operatorname{Gal}(K_\pi/K)\simeq\varprojlim_n(\mathcal O_K/\pi^n)^{\times}\simeq\mathcal O_K^{\times}
$$
as topological groups. This describes the <Galois group> without invoking local reciprocity.
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