German Title: IwasawaTheorie padischer LieErweiterungen

PDF, English
Download (669kB)  Terms of use 
Translation of abstract (English)
The Iwasawa theory of padic Lie groups investigates arithmetic objects above infinite field extensions of a number field k whose Galois group is a padic analytic group. The most prominent example (due to Serre) is produced by adjoining the ptorsion points of an elliptic curve defined over k without complex multiplication. The strategy consists in considering the Selmer Group or other cohomology groups which 'live' above the padic Lie extension as a module over the (noncommutative) group algebra R of G with coefficients in the padic integers. In the first, algebraic part of this dissertation special properties of R and of finitely generated Rmodules are studied. In particular, we introduce the notation of pseudonull modules as well as pseudoisomorphisms, which turn out to be essential for structure theorems of Rmodules. Then a local duality theorem and the AuslanderBuchsbaum equality for R are proved. In the second, arithmetic part we show the existence of certain pseudoisomorphisms of global Iwasawa modules, we study the µinvariant and we prove for some Galois modules that they do not contain any nontrivial pseudonull submodules.
Item Type:  Dissertation 

Supervisor:  Wingberg, Prof. Dr. Kay 
Date of thesis defense:  14 March 2001 
Date Deposited:  28 Mar 2001 00:00 
Date:  2001 
Faculties / Institutes:  The Faculty of Mathematics and Computer Science > Department of Mathematics 
Subjects:  510 Mathematics 
Controlled Keywords:  IwasawaTheorie, GaloisKohomologie, Lokale Kohomologie, Elliptische Kurve 
Uncontrolled Keywords:  Abelsche Varietät , Auslander reguläre Ringe , AuslanderBuchsbaum GleichungAbelean variety , Auslander regular ring , GaloisCohomology , AuslanderBuchsbaum equality 