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Local class field theory via Lubin-Tate theory
Thesis (MSc (Mathematics))--Stellenbosch University, 2008.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2008
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| _version_ | 1867614137394135040 |
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| access_status_str | Open Access |
| author | Mohamed, Adam |
| author2 | Keet, Arnold |
| author_browse | Keet, Arnold Mohamed, Adam |
| author_facet | Keet, Arnold Mohamed, Adam |
| author_sort | Mohamed, Adam |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc (Mathematics))--Stellenbosch University, 2008. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/2043 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:47:15.645Z |
| 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:10019.1/2043 Local class field theory via Lubin-Tate theory Mohamed, Adam Keet, Arnold Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Dissertations -- Mathematics Theses -- Mathematics Class field theory Local fields (Algebra) Formal groups Lubin-Tate Theory Thesis (MSc (Mathematics))--Stellenbosch University, 2008. This is an exposition of the explicit approach to Local Class Field Theory due to J. Tate and J. Lubin. We mainly follow the treatment given in [15] and [25]. We start with an informal introduction to p-adic numbers. We then review the standard theory of valued elds and completion of those elds. The complete discrete valued elds with nite residue eld known as local elds are our main focus. Number theoretical aspects for local elds are considered. The standard facts about Hensel's lemma, Galois and rami cation theory for local elds are treated. This being done, we continue our discussion by introducing the key notion of relative Lubin-Tate formal groups and modules. The torsion part of a relative Lubin-Tate module is then used to generate a tower of totally rami ed abelian extensions of a local eld. Composing this tower with the maximal unrami ed extension gives the maximal abelian extension: this is the local Kronecker-Weber theorem. What remains then is to state and prove the theorems for explicit local class eld theory and end our discussion. 2008-11-24T14:46:53Z 2010-06-01T08:39:25Z 2008-11-24T14:46:53Z 2010-06-01T08:39:25Z 2008-12 Thesis http://hdl.handle.net/10019.1/2043 en Stellenbosch University application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Dissertations -- Mathematics Theses -- Mathematics Class field theory Local fields (Algebra) Formal groups Lubin-Tate Theory Mohamed, Adam Local class field theory via Lubin-Tate theory |
| title | Local class field theory via Lubin-Tate theory |
| title_full | Local class field theory via Lubin-Tate theory |
| title_fullStr | Local class field theory via Lubin-Tate theory |
| title_full_unstemmed | Local class field theory via Lubin-Tate theory |
| title_short | Local class field theory via Lubin-Tate theory |
| title_sort | local class field theory via lubin tate theory |
| topic | Dissertations -- Mathematics Theses -- Mathematics Class field theory Local fields (Algebra) Formal groups Lubin-Tate Theory |
| url | http://hdl.handle.net/10019.1/2043 |
| work_keys_str_mv | AT mohamedadam localclassfieldtheoryvialubintatetheory |