The Lubin–Tate Formal Module in a Cyclic Unramified P-Extension as a Galois Module

Abstract

In the paper, the structure of the \( \mathcal{O} \)_K[G]-module F(\( \mathfrak{m} \)_M) is described, where M/L, L/K, and K/ℚ_p are finite Galois extensions (p is a fixed prime number), G = Gal(M/L), \( \mathfrak{m} \)_M is a maximal ideal of the ring of integers \( \mathcal{O} \)_M, and F is a Lubin–Tate formal group law over the ring \( \mathcal{O} \)_K for a fixed uniformizer π.