Hill's theorem of formal groups : applications, generalizations and counterexamples

One-dimensional formal groups were classified by W. Hill who showed in particular that one-dimensional formal groups are isomorphic over p-adic integers if and only if they have the same associated Eisenstein polynomial. This result can be applied to show that the torsion points on any supersingular elliptic curve over the field of p-adic numbers generate abelian extensions of the unramified quadradic extension of the field. The theorem cannot be extended to classify formal groups of higher dimension. Counterexamples will be provided both in the case of two-dimensional formal groups and when the formal group is defined over an extension of the p-adic integers. Constructions and classifications of higher dimensional formal groups due to T. Nakamura and M. Hazewinkel will also be explored