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Permanent link (DOI): https://doi.org/10.7939/R3CR5NM4M

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ON THE GALOIS STRUCTURE OF THE S-UNITS FOR CYCLOTOMIC EXTENSIONS OVER Q Open Access

Descriptions

Other title
Subject/Keyword
Cohomology
Algebraic number theory
Number theory
Envelopes
invariant maps
S-units
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Riveros Pacheco, David Ricardo
Supervisor and department
A.Weiss
Examining committee member and department
Alfred, Weiss (Department of Mathematical and Statistical Scinces)
Cristian, Popescu (Department of Mathematics UCSD)
Vladimir, Troitsky (Department of Mathematical and Statistical Scinces)
Nicolas, Guay (Department of Mathematical and Statistical Scinces)
Vladimir, Chernousov (Department of Mathematical and Statistical Scinces)
Charles, Doran (Department of Mathematical and Statistical Scinces)
Department
Department of Mathematical and Statistical Sciences
Specialization
mathematics
Date accepted
2015-09-28T14:44:08Z
Graduation date
2015-11
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
For K/k a finite Galois extension of number fields with G=Gal(K/k) and S a finite G-stable set of primes of K which is "large", Gruenberg and Weiss proved that the ZG-module structure of the S-units of K is completely determined up to stable isomorphism by: its torsion submodule, the set S, a particular character and the Chinburg class. In this Thesis, we will discuss the possibility of explicitly finding a ZG-module in the same stable isomorphism class of the S-units of K, in the particular case when k is the field of rational numbers and K is a cyclotomic extension over k.
Language
English
DOI
doi:10.7939/R3CR5NM4M
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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