Witt-Burnside ring and Burnside ring over a special λ-ring

초록

Given an arbitrary group G, we construct a covariant functor (F) over cap (G) from the category of special lambda-rings to that of commutative rings with unity. When G is a strongly complete profinite group, it will be used to reconstruct the functor Nr(G), which was first introduced in [Y.-T. Oh, R-analogue of the Burnside ring of profinite groups and free Lie algebras, Adv. Math. 190 (2005) 1-46] to investigate the structure of Witt-Burnside rings over special lambda-rings. More precisely, given a special lambda-ring R, we show that Nr(G)(R) is functorially isomorphic to (F) over cap (R)/J(G)(R) for some ideal J(G)(R) of (F) over cap (R). The connection to the functor F-G due to [J.J. Graham, Generalized Witt vectors, Adv. Math. 99 (1993) 248-263] will also be demonstrated. (C) 2012 Elsevier Inc. All rights reserved.

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