On Fitting ideals of certain étale \(K\)-groups
type: Item
instance of: scholarly article
title: On Fitting ideals of certain étale \(K\)-groups
zbMATH Open document ID: 1083.11073
DOI: 10.1023/A:1021629503427
author: Matthieu Le Floc'h
published in: \(K\)-Theory
publication date: 2003-04-27T00:00:00Z
review text: The author computes the first Fitting ideal of \(K^{\text{ét}}_{2i-2} (O^S_F) (\phi)\), showing it is principal and generated by a Brumer-Stickelberger element, where \(O^S_F\) is the \(S\)-integer ring of the abelian number field \(F/\mathbb{Q},\;\) \(S\) is a set of primes of \(F\) tamely or wildly ramified over the odd prim number \(p\), \(\phi\) is a character of Gal\((F/\mathbb{Q})\) of order prime to \(p\) different from the \(i\)th power of the Teichmüller character, and \(H(\phi)\) means \(e_\phi H\) with \(e_\phi\) the usual orthogonal idempotent.
Mathematics Subject Classification ID: 11R70
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 19D50
Mathematics Subject Classification ID: 19F27
zbMATH DE Number: 1901486
zbMATH Keywords: K-theory étale K-group
zbMATH Keywords: Fitting ideal
zbMATH Keywords: Iwasawa module
zbMATH Keywords: Stickelberger element
reviewed by: Xianke Zhang
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1901486