The Burnside ring of profinite groups and the Witt vector construction. (English) Zbl 0691.13026
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) [E. Witt, J. Reine Angew. Math. 176, 126-140 (1936; Zbl 0016.05101)]. Then 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.
Reviewer: M.Golasiński
MSC:
| 13K05 | Witt vectors and related rings (MSC2000) |
| 20E18 | Limits, profinite groups |
| 18F30 | Grothendieck groups (category-theoretic aspects) |
| 20C15 | Ordinary representations and characters |
References:
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