Micro primes
type: Item
instance of: scholarly article
title: Micro primes
zbMATH Open document ID: 0826.11053
DOI: 10.1007/BF01459755
author: Jürgen Neukirch
published in: Mathematische Annalen
publication date: 1995-11-27T00:00:00Z
full work available at URL: https://eudml.org/doc/165190
review text: In his book ``Class field theory'' [Springer Verlag Berlin (1986; Zbl 0587.12001)] the author develops class field theory on a group theoretical basis with a surprisingly easy definition of the reciprocity map using the characterization of this map by means of Durchkreuzung the given extension with a special extension, which in the local case is unramified and in the global case cyclotomic [see e.g. \textit{J. P. Serre}, Local class field theory, p. 145, in Algebraic Number Theory, Academic Press, London (1967; Zbl 0153.074)]. The definition of the reciprocity map by the author depends on the choice of a certain ``prime element''. In his present paper the author develops the concept of microprimes for a better understanding of the independence of the reciprocity map of the choice of the prime element. A microprime is a certain conjugacy class in a valued group. In this rather general setting one has a theory of decomposition groups of microprimes and other features known from algebraic number theory.
Mathematics Subject Classification ID: 11R37
zbMATH DE Number: 562481
zbMATH Keywords: reciprocity map
zbMATH Keywords: microprimes
zbMATH Keywords: conjugacy class
zbMATH Keywords: valued group
zbMATH Keywords: decomposition groups
reviewed by: Helmut Koch
MaRDI profile type: Publication
cites work: Q4097455
cites work: Axiomatic representation threory for finite groups
cites work: Q4001587
OpenAlex ID: W4250819047
description: scientific article; zbMATH DE number 562481