eprintid: 28383
rev_number: 14
eprint_status: archive
userid: 5034
dir: disk0/00/02/83/83
datestamp: 2020-06-05 13:36:58
lastmod: 2020-06-08 12:48:52
status_changed: 2020-06-05 13:36:58
type: doctoralThesis
metadata_visibility: show
creators_name: Kupferer, Benjamin Josef
title: Two ways to compute Galois Cohomology using Lubin-Tate (φ, Γ)-modules, a Reciprocity Law and a Regulator Map
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
keywords: (φ,Γ)-Moduln
cterms_swd: Algebraische Zahlentheorie
abstract: The main focus of the present thesis lays on general Lubin-Tate (φ,Γ)-modules. Before heading towards this theory, we discuss some general facts about monoid and continuous group cohomology as well as double complexes and limits of complexes. After these preliminaries we first show as in the classical case that the category of étale (φ,Γ)-modules is equivalent to the category of Galois representations of the absolute Galois group of K with coefficients in O_L, where K|L and L|Q_p are finite extensions. Using (φ, Γ)-modules, we then compute Iwasawa cohomology of such a representation and define a reciprocity map. Afterwards we compute the Galois cohomology groups using (φ, Γ)-modules. To do this, we construct two complexes of (φ, Γ)-modules whose cohomologies each coincide with the cohomology of the attached Galois representation. One of these two complexes is constructed by using the operator φ the other one by using the operator ψ. Finally, we construct a regulator map for an O_L × Z_p-extension of L.
date: 2020
id_scheme: DOI
id_number: 10.11588/heidok.00028383
ppn_swb: 1700164562
own_urn: urn:nbn:de:bsz:16-heidok-283834
date_accepted: 2020-05-29
advisor: HASH(0x561a62956568)
language: eng
bibsort: KUPFERERBETWOWAYSTOC2020
full_text_status: public
place_of_pub: Heidelberg
citation:   Kupferer, Benjamin Josef  (2020) Two ways to compute Galois Cohomology using Lubin-Tate (φ, Γ)-modules, a Reciprocity Law and a Regulator Map.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/28383/1/Two%20ways%20to%20compute%20Galois%20Cohomology%20using%20Lubin-Tate%20%28%CF%86%2C%20%CE%93%29-modules%2C%20a%20Reciprocity%20Law%20and%20a%20Regulator%20Map.pdf