Lubin–Tate tower ($K_{\pi }={\bigcup }_{n\ge 1}{K}_{\pi ,n}$)

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 givesas topological groups. This describes the Galois group without invoking local reciprocity.