Fitting ideals of isotypic parts of even K-groups
type: Item
instance of: scholarly article
title: Fitting ideals of isotypic parts of even K-groups
zbMATH Open document ID: 1414.11138
author: Saad El Boukhari
published in: Manuscripta Mathematica
publication date: 2018-09-14T00:00:00Z
review text: Let \(F\) be a real abelian number field with Galois group \(G=\mathrm{Gal}(F/\mathbb{Q})\). Let \(p\) be an odd prime and let \(m\geq 3\) be an odd integer. For certain \(p\)-adic characters \(\chi\) of \(G\), the author proves a formula relating the Fitting ideal of the (Pontyragin) dual of the \(\chi\)-part of \((K_{2m-1}(O_F)\otimes \mathbb{Z}_p)/D_{p,m}(F)\) to the Fitting ideal of the \(\chi\)-part of \(K_{2m-1}(O_F)\). Here \(D_{p,m}(F)\) is the \(\mathbb{Z}_p[G]\)-submodule of `Déligne-Soulé' elements of \(K_{2m-1}(O_F)\otimes\mathbb{Z}_p\), analogues of cyclotomic units. This formula should be considered as a refinement of known results comparing the orders of these modules. The author proceeds by calculating Fitting ideals of \(\chi\)-parts of certain Galois-equivariant Iwasawa modules and then relating these to the desired result by co-descent arguments.
reviewed by: Kevin Hutchinson
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R70
Mathematics Subject Classification ID: 19F27
zbMATH DE Number: 6936102
zbMATH Keywords: K-theory
zbMATH Keywords: algebraic number fields
zbMATH Keywords: Fitting ideals
zbMATH Keywords: Iwasasa theory
MaRDI profile type: Publication
full work available at URL: s00229-017-0991-y
OpenAlex ID: W2772901454
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DOI: 10.1007/S00229-017-0991-Y
description: scientific article; zbMATH DE number 6936102