= Lubin–Tate formal group
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{title2=$\mathcal F_f$}
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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; $[\pi]_f=f$.
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