Local class field theory via Lubin-Tate theory

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dc.contributor.advisorKeet, Arnold
dc.contributor.authorMohamed, Adam
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
dc.date.accessioned2008-11-24T14:46:53Zen_ZA
dc.date.accessioned2010-06-01T08:39:25Z
dc.date.available2008-11-24T14:46:53Zen_ZA
dc.date.available2010-06-01T08:39:25Z
dc.date.issued2008-12
dc.descriptionThesis (MSc (Mathematics))--Stellenbosch University, 2008.
dc.description.abstractThis 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.en
dc.identifier.urihttp://hdl.handle.net/10019.1/2043
dc.language.isoen
dc.publisherStellenbosch : Stellenbosch University
dc.rights.holderStellenbosch University
dc.subjectDissertations -- Mathematicsen
dc.subjectTheses -- Mathematicsen
dc.subjectClass field theoryen
dc.subjectLocal fields (Algebra)en
dc.subjectFormal groupsen
dc.subjectLubin-Tate Theoryen
dc.titleLocal class field theory via Lubin-Tate theoryen
dc.typeThesis
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