Galois Module Structure Of Lubin-Tate Modules

Let L/K be a finite, Galois extension of local or global fields. In the classical setting of additive Galois modules, the ring of integers O L of L is studied as a module for the group ring O K G, where G is the Galois group of L/K. When K is a p-adic field, we also find a structure of O K G module when we replace O L with the group of points in O L of a Lubin-Tate formal group defined over K. For this new Galois module we find an analogue of the normal basis theorem. When K is a proper unramified extension of Q p , we show that some eigenspaces for the Teichm�ller character are not free. We also adapt certain cases of E. Noether’s result on normal integral bases for tame extensions. Finally, for wild extensions we define a version of Leopoldt’s associated order and demonstrate in a specific case that it is strictly larger than the integral group ring.