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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/2043 |
| Date | 12 1900 |
| Creators | Mohamed, Adam |
| Contributors | Keet, Arnold, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | Stellenbosch University |
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