Chromatic characteristic classes in ordinary group cohomology
David J. Green 
John R. Hunton 
Bj"orn Schuster 
Submitted for publication, Aug. 2001

Abstract:
We study a family of subrings, indexed by the natural
numbers, of the mod-p cohomology of a finite group G.
These 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)).

Note:
Supersedes the Dec. 1998 paper of the same name by Green and Schuster.