Cohomology of class groups of cyclotomic fields; an application to Morse- Smale diffeomorphisms
type: Item
instance of: scholarly article
title: Cohomology of class groups of cyclotomic fields; an application to Morse- Smale diffeomorphisms
zbMATH Open document ID: 0651.12004
DOI: 10.1016/0022-4049(88)90016-3
author: René Schoof
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: The author is concerned with describing the 2-part of \(SSF=K_ 0({\mathcal C})/P\) where \(K_ 0({\mathcal C})\) is the Grothendieck group of object pairs (H,u) with H a finitely generated abelian group, and \(u\in Aut(H)\); and where P is the subgroup generated by the classes of permutation modules. SSF is abelian except for its 2-part. Finally the author looks specifically at the Galois cohomology of the 2-part of class groups of abelian number fields and applies these results to the class groups of the fields in the cyclotomic \({\mathbb{Z}}_ 2\)-extension of \({\mathbb{Q}}(\zeta_{16})\).
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 18F30
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R34
zbMATH DE Number: 4061349
zbMATH Keywords: obstructions for Morse-Smale diffeomorphisms
zbMATH Keywords: Grothendieck group
zbMATH Keywords: class groups of abelian number fields
zbMATH Keywords: cyclotomic \({\mathbb{Z}}_ 2\)-extension
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90016-3
OpenAlex ID: W1981040604
cites work: Q3968159
cites work: The class group of all cyclotomic integers
cites work: Q5532660
cites work: Q3939901
cites work: The existence of Morse-Smale diffeomorphisms
cites work: Q4177670
cites work: Grothendieck groups of Abelian group rings
cites work: Q5597002
cites work: Homology theory and dynamical systems
cites work: Q5690489
cites work: On unramified Galois extensions of quadratic number fields
description: scientific article; zbMATH DE number 4061349