eprintid: 1451
rev_number: 8
eprint_status: archive
userid: 1
dir: disk0/00/00/14/51
datestamp: 2001-03-28 00:00:00
lastmod: 2014-04-03 10:47:57
status_changed: 2012-08-14 15:01:20
type: doctoralThesis
metadata_visibility: show
creators_name: Venjakob, Otmar
title: Iwasawa theory of p-adic Lie extensions
title_de: Iwasawa-Theorie p-adischer Lie-Erweiterungen
ispublished: pub
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
keywords: Abelsche Varietät , Auslander reguläre Ringe , Auslander-Buchsbaum GleichungAbelean variety , Auslander regular ring , Galois-Cohomology , Auslander-Buchsbaum equality
cterms_swd: Iwasawa-Theorie
cterms_swd: Galois-Kohomologie
cterms_swd: Lokale Kohomologie
cterms_swd: Elliptische Kurve
abstract_translated_text: 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.
abstract_translated_lang: eng
class_scheme: msc
class_labels: 14K15, 11G05, 11R23, 12G05, 16S34
date: 2001
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00001451
ppn_swb: 1643245708
own_urn: urn:nbn:de:bsz:16-opus-14512
date_accepted: 2001-03-14
advisor: HASH(0x561a6286bcf0)
language: eng
bibsort: VENJAKOBOTIWASAWATHE2001
full_text_status: public
citation:   Venjakob, Otmar  (2001) Iwasawa theory of p-adic Lie extensions.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/1451/1/THESIS.pdf