Iwasawa theory of p-adic Lie extensions

The Iwasawa theory of p-adic Lie groups investigates arithmetic objects above infinite field extensions of a number field k whose Galois group is a p-adic analytic group. The most prominent example (due to Serre) is produced by adjoining the p-torsion 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 p-adic Lie extension as a module over the (non-commutative) group algebra R of G with coefficients in the p-adic integers. In the first, algebraic part of this dissertation special properties of R and of finitely generated R-modules are studied. In particular, we introduce the notation of pseudo-null modules as well as pseudo-isomorphisms, which turn out to be essential for structure theorems of R-modules. Then a local duality theorem and the Auslander-Buchsbaum equality for R are proved. In the second, arithmetic part we show the existence of certain pseudo-isomorphisms of global Iwasawa modules, we study the µ-invariant and we prove for some Galois modules that they do not contain any non-trivial pseudo-null submodules.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Heidelberg

Year

2001

Author dc:creator

• Venjakob, Otmar

Contributors dc:contributor

• Wingberg, Kay

Repository record source_url

http://www.ub.uni-heidelberg.de/archiv/1451

OAI identifier oai:identifier

oai:archiv.ub.uni-heidelberg.de:1451