Date of Award

2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mathematics

First Advisor

Ted Chinburg

Abstract

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.

Included in

Mathematics Commons

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