 Lubin–Tate formal group

A Lubin–Tate formal group associated with a Lubin–Tate series $f$ is the unique one-dimensional commutative formal group law ${\mathcal{F}}_f$ over the valuation ring ${\mathcal{O}}_K$ for which $f$ is an endomorphism with linear coefficient the chosen uniformizer $\pi$. The Lubin–Tate functional equation lemma constructs the law and the endomorphisms $[a{]}_f$ for every $a\in {\mathcal{O}}_K$, with linear term $aX$. Their addition is given by the law, and their multiplication by composition. Thus the valuation ring acts on the group; $[\pi {]}_f=f$.