On two-dimensional formal groups over the prime field of characteristic p > 0

Abstract

In what follows, by a formal group we always mean a commutative one. In Hill [6], the following result (Theorem E’) is proved: Let F and G be onedimensional formal groups over F,,, the prime field of characteristic p > 0. If F and G are of finite height and have the same characteristic polynomial, then F and G are isomorphic over F,. For two-dimensional formal groups over F,, this is not valid in general. A counterexample is given in Section 4. Using a result on a classification of two-dimensional formal groups due to Ditters [4], we shall show in Section 2 that for certain types of formal groups, the above result is also valid (Corollary 1 of Theorem 1). In Section 3, we shall determine the simple twodimensional formal groups over F, whose endomorphism rings are maximal orders. Some examples are discussed in Section 4.