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On the structure of the absolute Galois group of local fields with residue characteristic 2

Schneider, Franziska (2016) On the structure of the absolute Galois group of local fields with residue characteristic 2. PhD, Universität Regensburg.

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Date of publication of this fulltext: 15 Dec 2016 08:59

Abstract (English)

In this thesis we give a description in terms of generators and relations of the Galois group of the maximal extension without simple ramification of a local field k with residue characteristic 2. Furthermore, we assume that the fourth roots of unity are not contained in the maximal tamely ramified extension of k and that k is of even degree over the field of 2-adic numbers. For fields of odd degree this has been done by Zelvenskii. Our proof uses methods similar to his.

Translation of the abstract (German)

In dieser Arbeit geben wir eine Beschreibung der Galois Gruppe der maximalen Erweiterung ohne zahme Verzweigung eines 2-adischen Zahlkörpers k durch Erzeugende und Relationen. Zudem nehmen wir an, dass die vierten Einheitswurzeln nicht in der maximalen zahmverzweigten Erweiterung von k liegen und k geraden Grad über dem Körper der 2-adischen Zahlen hat. Für Körper von ungeradem Grad wurde dies ...

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Item type:Thesis of the University of Regensburg (PhD)
Date:15 December 2016
Referee:Prof. Dr. Uwe Jannsen
Date of exam:8 December 2016
Institutions:Mathematics > Prof. Dr. Uwe Jannsen
Keywords:absolute Galois group, extension without simple ramification, local fields of residue characteristic 2
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:34985
Owner only: item control page

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