Model theory of absolute Galois groups [Elektronische Ressource] / vorgelegt von Nina Frohn

Model Theory of AbsoluteGalois GroupsDissertationzur Erlangung des Doktorgradesder Fakultat˜ fur˜ Mathematik und Physikder Albert{Ludwigs{Universitat˜ Freiburgvorgelegt vonNina FrohnFreiburg, Januar 2011Dekan: Prof. Dr. Kay Konigsmann˜Erster Gutachter: Dr. Jochen KoenigsmannZweiter Gutachter: Prof. Dr. Martin ZieglerDatum der Promotion: 10.12.2010Abteilung fur Mathematische Logik˜Fakultat fur Mathematik und Physik˜ ˜Albert-Ludwigs-Universitat Freiburg˜Eckerstra…e 179104 Freiburg i. Br.IntroductionGaloistheoryisalivelyareaofmathematicalresearchinwhichseveralbranchesof mathematics (as algebra, number theory and geometry) are involved. Thisthesis is concerned with the model theoretic aspects of Galois theory, and inparticular with the model theoretic aspects of the universal object of Galoistheory, the absolute Galois group.Model theory often studies elementary classes of flrst-order structures, or aclassofflrst-orderstructuressharingsomemodel-theoreticproperty.Thecentralquestion in the background of this work is the question whether or not theclass of absolute Galois groups is an elementary class in an appropriate flrst-order language. The answer is likely to be negative: The general group theoreticstructureofabsoluteGaloisgroupsisnotknownverywell,andthereisnogrouptheoretical characterization of those proflnite groups which occur as absoluteGalois groups, not even conjecturally.