Explicit class field theory for rational function fields

Autor:	Rakotoniaina, Tahina
Jazyk:	angličtina
Rok vydání:	2008
Předmět:	Class field theory Function fields Drinfeld modules Carlitz module Number theory Theses Mathematics Dissertations Numbers Rational Cyclotomic fields Function algebras Field extensions (Mathematics) Mathematical Sciences
Druh dokumentu:	Diplomová práce
Popis:	Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008. 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.
Databáze:	Networked Digital Library of Theses & Dissertations
Externí odkaz:	http://hdl.handle.net/10019.1/2143 Zobrazit plný text záznamu