Galois module structure of non-Kummer extensions

Abstract

Let L/K be extensions of the p-adic field ℚp. We show that when L and K are division fields of a Lubin-Tate formal group, then D fractur signL, the ring of integers in L is a free rank one module over the associated order ΘL/K. Chan and Lim had previously determined ΘL/K without obtaining any structure results for D fractur signL, except in the cyclotomic case. This extends, in the local case, previous results of Leopoldt, Chan and Lim, and Taylor.