Honda formal group as Galois module in unramified extensions of local fields

Abstract

For given rational prime number p consider the tower of finite extensions of fields K 0 /Q p , K/K 0 , L/K, M/L, where K/K 0 is unramified and M/L is a Galois extension with Galois group G. Suppose one dimensional Honda formal group over the ring O K , relative to the extension K/K 0 and uniformizer π ∈ K 0 is given. The operation x + F y = F (x, y) sets a new structure of abelian group on the maximal ideal p M of the ring O M which we will denote by F (p M ). In this paper the structure of F (p M ) as O K 0 [G]-module is studied for specific unramified p-extensions M/L.