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Pro-endliche Gruppen

Lemmermeyer, Franz

English Title: Profinite Groups

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Abstract

Unter Voraussetzung der endlichen Galoistheorie wird die Galoistheorie unendlicher algebraischer Erweiterungen besprochen und der Hauptsatz bewiesen. Im Anschluss daran werden projektive Limites definiert und einige funktorielle Eigenschaften bewiesen. Die Kapitel 3 und 4 sind dann der Galois-Kohomologie pro-endlicher Gruppen gewidmet; als Anwendung wird die ambige Klassenzahlformel fuer quadratische Zahlkoerper hergeleitet.

Translation of abstract (English)

Assuming the finite Galois theory as known, we discuss the Galois theory of infinite algebraic extensions and prove its main theorem. Then we introduce projective limits and discuss some of their functorial properties. Chapters 3 and 4 contain elements of the Galois cohomology of profinite groups; as an application, we prove the ambiguous class number formula for quadratic number fields.

Item Type: Other
Date Deposited: 16. Aug 1999 13:55
Date: 1999
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Mathematics
Subjects: 510 Mathematics
Controlled Keywords: Proendliche Gruppe, Galois-Theorie, Galois-Kohomologie, Projektiver Limes, Geschlecht <Mathematik>
Uncontrolled Keywords: profinite groups, Galois cohomology, infinite extensions, ambiguous ideal classes, projective limits
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