The Burnside ring of profinite groups and the Witt vector construction
type: Item
instance of: scholarly article
title: The Burnside ring of profinite groups and the Witt vector construction
zbMATH Open document ID: 0691.13026
DOI: 10.1016/0001-8708(88)90052-7
author: Christian Siebeneicher
author: Andreas W. M. Dress
published in: Advances in Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let G be an arbitrary profinite group. The authors construct a functor \(W_ G\) from the category of commutative rings to itself such that \(W_ G({\mathbb{Z}})\simeq {\hat \Omega}(G)\), where \({\hat \Omega}\)(G) is the completed Burnside ring. If \(G=\hat C\) (resp. \(\hat C_ p)\) the profinite (resp. pro-p-) completion of the infinite cyclic group C then W(\({\mathbb{Z}})\simeq {\hat \Omega}(\hat C)\) (resp. \(W_ p({\mathbb{Z}})\simeq {\hat \Omega}(\hat C_ p))\), where W (resp. \(W_ p)\) is the classical Witt vector construction (resp. p-construction) [\textit{E. Witt}, J. Reine Angew. Math. 176, 126-140 (1936; Zbl 0016.05101)]. Then \textit{P. Cartier}'s result [C. R. Acad. Sci., Paris, Sér. A 265, 49-52 (1967; Zbl 0168.275)] is a special instance of a far more general fact.
reviewed by: Marek Golasiński
Mathematics Subject Classification ID: 13K05
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 18F30
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 4130527
zbMATH Keywords: Burnside ring of profinite groups
zbMATH Keywords: Witt vector
MaRDI profile type: Publication
full work available at URL: 0001-8708(88)90052-7
OpenAlex ID: W2036214024
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description: scientific article; zbMATH DE number 4130527