### Chromatic characteristic classes in ordinary group cohomology, by David J. Green, John R. Hunton, and Bjoern Schuster

We study a family of subrings, indexed by the natural
numbers, of the mod-p cohomology of a finite group G.
hese subrings are based on a family of v_{n}-periodic
complex oriented cohomology theories and are constructed as
rings of generalised characteristic classes. We identify the
varieties associated to these subrings in terms of colimits
over categories of elementary abelian subgroups of G,
naturally interpolating between the work of Quillen on
var(H^{*}(BG)), the variety of the whole
cohomology ring, and that of Green and Leary on the variety
of the Chern subring, var(Ch(G)). Our subrings give rise
to a "chromatic" (co)filtration, which has both
topological and algebraic definitions, of var(H^{*}(BG))
whose final quotient is the variety var(Ch(G)).

David J. Green <green@math.uni-wuppertal.de>

John R. Hunton <J.Hunton@mcs.le.ac.uk>

Bjoern Schuster <schuster@math.uni-wuppertal.de>