Algebraic & Geometric Topology 6 (2006) 253–285

DOI: 10.2140/agt.2006.6.253

arXiv: 0902.4867

Abstract

In this paper, we examine the "derived completion" of the representation ring of a pro–p group G_p^ with respect to an augmentation ideal. This completion is no longer a ring: it is a spectrum with the structure of a module spectrum over the Eilenberg–MacLane spectrum HZ, and can have higher homotopy information. In order to explain the origin of some of these higher homotopy classes, we define a deformation representation ring functor R[–] from groups to ring spectra, and show that the map R[G_p^]→R[G] becomes an equivalence after completion when G is finitely generated nilpotent. As an application, we compute the derived completion of the representation ring of the simplest nontrivial case, the p–adic Heisenberg group.

Keywords

S-algebra, R-module, completion, Bousfield localization, representation ring

Mathematical Subject Classification

Primary: 55P60

Secondary: 19A22, 55P43

References

Forward citations

Publication

Received: 11 April 2005
Revised: 31 October 2005
Accepted: 5 January 2006
Published: 26 February 2006

Authors