Generalized Burnside-grothendieck Ring Functor and Aperiodic Ring Functor Associated with Profinite Groups
نویسنده
چکیده
For every profinite group G, we construct two covariant functors ∆G and APG from the category of commutative rings with identity to itself, and show that indeed they are equivalent to the functor WG introduced in [A. Dress and C. Siebeneicher, The Burnside ring of profinite groups and the Witt vectors construction, Adv. Math. 70 (1988), 87-132]. We call ∆G the generalized Burnside-Grothendieck ring functor and APG the aperiodic ring functor (associated with G). In case G is abelian, we also construct another functor ApG from the category of commutative rings with identity to itself as a generalization of the functor Ap introduced in [K. Varadarajan, K. Wehrhahn, Aperiodic rings, necklace rings, and Witt vectors, Adv. Math. 81 (1990), 129]. Finally it is shown that there exist q-analogues of these functors (i.e, WG, ∆G, APG, and ApG) in case G = Ĉ the profinite completion of the multiplicative infinite cyclic group.
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