The Structure of Formal Modules as Galois Modules in Cyclic Unramified p-Extensions

Abstract

The structure of a formal module F( $$ \mathfrak{M} $$ ) for a chain of finite extensions M/L/K, where M/L is an unramified p-extension, is studied. It is proved that the first Galois cohomology of a formal module for an unramified extension is trivial for any degree of prime ideal. The presentation of the formal module is constructed in terms of generators and relations. As an application of the main result, the structure of a formal module for generalized Lubin–Tate formal groups is obtained.