The Burnside ring of profinite groups and the Witt vector construction
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.
scientific article; zbMATH DE number 4130527