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On nilpotent extensions of algebraic number fields I

Published online by Cambridge University Press:  22 January 2016

Katsuya Miyake  and
Hans Opolka
Katsuya Miyake*
Affiliation:
Department of Mathematics College of General Education Nagoya University, Nagoya, 464-01, Japan
Hans Opolka*
Affiliation:
Mathematisches Institut Universität Göttingen, Bunsenstrasse 3-5 D-3400 Göttingen, B.R.D.
*
Institut für Algebra und Zahlentheorie Technische UniversitätBraunschweig Pockelsstraße 14 D-W-3300 BraunschweigB.R.D.
Institut für Algebra und Zahlentheorie Technische UniversitätBraunschweig Pockelsstraße 14 D-W-3300 BraunschweigB.R.D.
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The lower central series of the absolute Galois group of a field is obtained by iterating the process of forming the maximal central extension of the maximal nilpotent extension of a given class, starting with the maximal abelian extension. The purpose of this paper is to give a cohomological description of this central series in case of an algebraic number field. This description is based on a result of Tate which states that the Schur multiplier of the absolute Galois group of a number field is trivial. We are in a profinite situation throughout which requires some functorial background especially for treating the dual of the Schur multiplier of a profinite group. In a future paper we plan to apply our results to construct a nilpotent reciprocity map.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 125 , March 1992 , pp. 1 - 14
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

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