Explicit class field theory for rational function fields
Date
2008-12
Authors
Rakotoniaina, Tahina
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : Stellenbosch University
Abstract
Class field theory describes the abelian extensions of a given field K in terms of various
class groups of K, and can be viewed as one of the great successes of 20th century
number theory. However, the main results in class field theory are pure existence
results, and do not give explicit constructions of these abelian extensions. Such
explicit constructions are possible for a variety of special cases, such as for the field Q
of rational numbers, or for quadratic imaginary fields. When K is a global function
field, however, there is a completely explicit description of the abelian extensions of
K, utilising the theory of sign-normalised Drinfeld modules of rank one. In this thesis
we give detailed survey of explicit class field theory for rational function fields over
finite fields, and of the fundamental results needed to master this topic.
Description
Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008.
Keywords
Class field theory, Function fields, Drinfeld modules, Carlitz module, Number theory, Theses -- Mathematics, Dissertations -- Mathematics