Genus theory and governing fields
type: Item
instance of: scholarly article
title: Genus theory and governing fields
zbMATH Open document ID: 1442.11155
author: Christian Maire
published in: The New York Journal of Mathematics
publication date: 2018-11-21T00:00:00Z
full work available at URL: 24-50.html
review text: Let \(L/K\) be a Galois extension of number fields. In this paper; the author develops an approach to the genus theory of \(L/K\) by introducing some governing field. When the restriction of each inertia group to the (local) abelianization is annihilated by a fixed prime number \(p\), this point of view allows the author to estimate the genus number of \(L/K\) with the aid of a subspace of the governing extension generated by some Frobenius elements. Then given a number field \(K\) and a possible genus number \(g\), the author derive information about the smallest prime ideals of \(K\) for which there exists a degree \(p\) cyclic extension \(L/K\) ramified only at these primes and having \(g\) as genus number.
reviewed by: Abdelmalek Azizi
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R45
zbMATH DE Number: 6982028
zbMATH Keywords: genus theory
zbMATH Keywords: governing field
zbMATH Keywords: Chebotarev density theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6982028