Date of Award
Doctor of Philosophy (PhD)
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.
Tomaskovic-Moore, Sebastian, "Galois Module Structure Of Lubin-Tate Modules" (2017). Publicly Accessible Penn Dissertations. 2612.