Teichmuller expansion
= Teichmuller expansion
If $K$ is a complete <discretely valued field> whose residue field $k$ is a <perfect field>, and $\pi$ is a <uniformizer>, the multiplicative Teichmuller lift $[\mathord\cdot]:k\to\mathcal O_K$ gives each $x\in\mathcal O_K$ a unique expansion
$$
x=\sum_{i=0}^{\infty}[a_i]\pi^i,
\qquad a_i\in k.
$$