Generalized Burnside-Grothendieck ring functor and aperiodic ring functor associated with profinite groups

Details Generalized Burnside-Grothendieck ring functor and aperiodic ring functor associated with profinite groups Generalized Burnside-Grothendieck ring functor and aperiodic ring functor associated with profinite groups

2004-05-21

arxiv.org/abs/math/0405400v2

Mathematics

Rings and Algebras

minor corrections, 35 pages

Scientific paper

For every profinite group $G$, we construct two covariant functors $\Delta_G$ and ${\bf {\mathcal {AP}}}_G$ from the category of commutative rings with identity to itself, and show that indeed they are equivalent to the functor $W_G$ introduced in [A. Dress and C. Siebeneicher, The Burnside ring of profinite groups and the Witt vectors construction, {\it Adv. in Math.} {\bf{70}} (1988), 87-132]. We call $\Delta_G$ the generalized Burnside-Grothendieck ring functor and ${\bf {\mathcal {AP}}}_G$ the aperiodic ring functor (associated with $G$). In case $G$ is abelian, we also construct another functor ${\bf Ap}_G$ from the category of commutative rings with identity to itself as a generalization of the functor ${\bf Ap}$ introduced in [K. Varadarajan, K. Wehrhahn, Aperiodic rings, necklace rings, and Witt vectors, {\it Adv. in Math.} {\bf 81} (1990), 1-29]. Finally it is shown that there exist $q$-analogues of these functors (i.e, $W_G, \Delta_G, {\bf {\mathcal {AP}}}_G$, and ${\bf Ap}_G$) in case $G=\hat C$ the profinite completion of the multiplicative infinite cyclic group.

Affiliated with

Also associated with

No associations

Rating

Generalized Burnside-Grothendieck ring functor and aperiodic ring functor associated with profinite groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Burnside-Grothendieck ring functor and aperiodic ring functor associated with profinite groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Burnside-Grothendieck ring functor and aperiodic ring functor associated with profinite groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-679778