 Lubin–Tate formal group

For a uniformizer $\pi$ of a local field $K$ with residue-field cardinality $q$, a Lubin–Tate series is a series $f(X)\in {\mathcal{O}}_K[[X]]$ satisfying $f(X)\equiv \pi X(\mathrm{mod}{X}^2)$ and $f(X)\equiv X^q(\mathrm{mod}\pi )$. It determines a unique one-dimensional commutative formal group law ${\mathcal{F}}_f$ on which every $a\in {\mathcal{O}}_K$ acts through an endomorphism $[a{]}_f$ with linear term $aX$.