Galois module structure of non-Kummer extensions

Abstract.

Let L / K be extensions of the p-adic field $\Bbb Q _p$. We show that when L and K are division fields of a Lubin-Tate formal group, then $\frak O _L$, the ring of integers in L is a free rank one module over the associated order $\frak U _{L/K}$. Chan and Lim had previously determined $\frak U _{L/K}$ without obtaining any structure results for $\frak O _L$, except in the cyclotomic case. This extends, in the local case, previous results of Leopoldt, Chan and Lim, and Taylor.