Formal multiplicative group
= Formal multiplicative group
{title2=$\widehat{\mathbb G}_m$}
The formal multiplicative group has law $F_m(X,Y)=X+Y+XY$, obtained by writing a multiplicative coordinate as $1+X$. Its multiplication-by-$n$ series is
$$
[n]_m(X)=(1+X)^n-1.
$$