 
Summary: BULLETIN (New Series) OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 6, Number 1, January 1982
RESEARCH ANNOUNCEMENTS
A QUILLEN STRATIFICATION THEOREM FOR MODULES
BY GEORGE S. AVRUNIN AND LEONARD L. SCOTT1
Let G be a finite group and k a fixed algebraically closed field of character
istic p > 0. If p is odd, let HG be the subring of //*(G, k) consisting of ele
ments of even degree; take HG = //*(G, k) if p = 2. HG is a finitely generated
commutativefcalgebra,and we let VG denote its associated affine variety Max HG.
If M is any finitely generatedfcGmodule,the cohomology variety VG(M) of M
may be defined as the support in VG of the HG module H*(G, M) if G is a p
group, and in general as the largest support of //*(G, L ® M) where L is any kG
module. A module L with each irreduciblefcGmoduleas a direct summand will
do [3].
D. Quillen [9, 10] proved a number of beautiful results relating VG to the
varieties VE associated with the elementary abelian psubgroups E of Gf culmin
ating in his stratification theorem. This theorem gives a piecewise description of
VG in terms of the subgroups E and their normalizers in G. Some of Quillen's
results have been extended to the variety VG(M) associated with a fcGmodule
