Explicit class field theory for rational function fields

dc.contributor.advisorBreuer, Florianen_ZA
dc.contributor.authorRakotoniaina, Tahinaen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
dc.descriptionThesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008.
dc.description.abstractClass 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.en_ZA
dc.publisherStellenbosch : Stellenbosch University
dc.subjectClass field theoryen_ZA
dc.subjectFunction fieldsen_ZA
dc.subjectDrinfeld modulesen_ZA
dc.subjectCarlitz moduleen_ZA
dc.subjectNumber theoryen_ZA
dc.subjectTheses -- Mathematicsen_ZA
dc.subjectDissertations -- Mathematicsen_ZA
dc.subject.lcshNumbers, Rationalen_ZA
dc.subject.lcshField extensions (Mathematics)
dc.subject.lcshCyclotomic fieldsen_ZA
dc.subject.lcshFunction algebrasen_ZA
dc.subject.otherMathematical Sciencesen_ZA
dc.titleExplicit class field theory for rational function fieldsen_ZA
dc.rights.holderStellenbosch University

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