= Lubin–Tate cyclotomic example
{c}
{title2=$\mathbb Q_p(\mu_{p^n})$}
For $K=\mathbb Q_p$ and $\pi=p$, choose the <Lubin–Tate series> $f(T)=(1+T)^p-1$. The associated <formal group law> is the <formal multiplicative group>. Its torsion points are $\zeta-1$ for $\zeta^{p^n}=1$, so its <Lubin–Tate extension> is the <cyclotomic extension of a p-adic field> $\mathbb Q_p(\mu_{p^n})$. The Galois action $\zeta\mapsto\zeta^a$ gives $(\mathbb Z/p^n\mathbb Z)^{\times}$, including the trivial first layer when $p=2$.
Back to article page
