On some congruences for units of local \(p\)-cyclotomic fields
type: Item
instance of: scholarly article
title: On some congruences for units of local \(p\)-cyclotomic fields
zbMATH Open document ID: 0867.11074
DOI: 10.1007/BF02940809
author: O. Diekmann
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1997-02-13T00:00:00Z
review text: Let \(p\) be prime, \(k_n\) the local \(p^{n+1}\)th cyclotomic field, \(K_\infty\) the union of these \(k_n\), \(U_n\) the group of principal units of \(k_n\), and \(B_n\) its subgroup of all units which are norms from every \(U_m\), \(m\geq n\). Moreover, let \(\chi\) be a \(\mathbb{Q}_p\)-valued character of \(\Delta=\text{Gal}(k_0/\mathbb{Q}_p)\), \(\Gamma=\text{Gal}(k_\infty/k_0)\) and \(\Lambda=\mathbb{Z}_p\Gamma\). The author studies the submodule \(J(n,a,\chi)\) of the \(\chi\)-eigenspace \(B_n(\chi)\) consisting of all units which are congruent to 1 modulo \((1-\xi)^a\), where \(\xi\) is a primitive \(p\)th root of unity. This generalizes earlier results of his [J. Reine Angew. Math. 462, 169-184 (1995; Zbl 0815.11055)], where the special case \(a=1\) was studied.
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R18
zbMATH DE Number: 977871
zbMATH Keywords: local cyclotomic fields
zbMATH Keywords: cyclotomic units
zbMATH Keywords: congruences
reviewed by: Franz Lemmermeyer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 977871