Swan Modules and Elliptic Functions

M. J. Taylor has described the additive Galois module structure of rings of integers of certain Kummer extensions with respect to an elliptic group law. He has obtained elliptic analogues of cyclotomic results. The arithmetic nature of elliptic resolvents, the elliptic analogue of the Gauss sum conductor formula and the strength of the elliptic group law being a Lubin-Tate formal group law enabled Taylor to show that the ring of algebraic integers is free over the associated order, if and only if, a certain elliptic analogue of a Swan module is a principal ideal of the associated order. In this thesis we find an explicit generator for the square of this elliptic Swan module in quite a general case. This generator is a product of elliptic resolvent elements.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Srivastav, Anupam

Contributors dc:contributor

• Ullom, Stephen V.

• Mathematics

Identifier

(UMI)AAI8803209

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71262