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Finite subgroups of formal groups /Schmitz, David John. January 2001 (has links)
Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2001. / Includes bibliographical references. Also available on the Internet.
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Deformation Theory of Non-Commutative Formal Groups in Positive CharacteristicLeitner, Frederick Carl January 2005 (has links)
We discuss the deformation theory of non-commutative formal groups G in positive characteristic. Under a geometric assumption on G, we produce a commutative formal group H whose distribution bialgebra has a certain skewed Poisson structure. This structure gives first order deformation data which integrates to the distribution bialgebra of G.
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Local Class Field Theory via Lubin-Tate Theory /Mohamed, Adam. January 2008 (has links)
Thesis (MSc)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.
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Local class field theory via Lubin-Tate theoryMohamed, Adam 12 1900 (has links)
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.
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