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.