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Explicit class field theory for rational function fields
Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2008
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| _version_ | 1867613886209851392 |
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| access_status_str | Open Access |
| author | Rakotoniaina, Tahina |
| author2 | Breuer, Florian |
| author_browse | Breuer, Florian Rakotoniaina, Tahina |
| author_facet | Breuer, Florian Rakotoniaina, Tahina |
| author_sort | Rakotoniaina, Tahina |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/2143 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:43:15.981Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/2143 Explicit class field theory for rational function fields Rakotoniaina, Tahina Breuer, Florian Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Class field theory Function fields Drinfeld modules Carlitz module Number theory Theses -- Mathematics Dissertations -- Mathematics Numbers, Rational Cyclotomic fields Function algebras Field extensions (Mathematics) Mathematical Sciences 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. 2008-11-26T09:56:33Z 2010-06-01T08:41:23Z 2008-11-26T09:56:33Z 2010-06-01T08:41:23Z 2008-12 Thesis http://hdl.handle.net/10019.1/2143 en Stellenbosch University application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Class field theory Function fields Drinfeld modules Carlitz module Number theory Theses -- Mathematics Dissertations -- Mathematics Numbers, Rational Cyclotomic fields Function algebras Field extensions (Mathematics) Mathematical Sciences Rakotoniaina, Tahina Explicit class field theory for rational function fields |
| title | Explicit class field theory for rational function fields |
| title_full | Explicit class field theory for rational function fields |
| title_fullStr | Explicit class field theory for rational function fields |
| title_full_unstemmed | Explicit class field theory for rational function fields |
| title_short | Explicit class field theory for rational function fields |
| title_sort | explicit class field theory for rational function fields |
| topic | Class field theory Function fields Drinfeld modules Carlitz module Number theory Theses -- Mathematics Dissertations -- Mathematics Numbers, Rational Cyclotomic fields Function algebras Field extensions (Mathematics) Mathematical Sciences |
| url | http://hdl.handle.net/10019.1/2143 |
| work_keys_str_mv | AT rakotoniainatahina explicitclassfieldtheoryforrationalfunctionfields |