Standard group

Definition

Over a local ring

Suppose $R$ is a local ring and $M$ is its unique maximal ideal. Suppose $F$ is a $d$-dimensional formal group law over $R$. The standard group over $R$ corresponding to $F$ is the group whose set of elements is given by the set of $d$-tuples over $M$ (which could be denoted $M^{d}$, but is not to be confused with the $d^{th}$ power of $M$ in $R$, hence is sometimes denoted $M^{(d)}$) and where the group operation is given by $F$.