 
Summary: Invent. math. 66, 277286 (1982) [nvel~tlol~e$
matbematicae
,i" SpringerVertag1982
Quillen Stratification for Modules
George S. Avrunin i and Leonard L. Scott .2
Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003,
USA
2 Department of Mathematics, Universityof Virginia,Charlottesville,VA 22903, USA
Introduction
Let G be a finite group and k a fixed algebraically closed field of characteristic
p>0. If p is odd, let H(; be the subring of H*(G,k) consisting of elements of
even degree; following [2022] we take H~=H*(G,k) if p=2, though one
could just as well use the subring of elements of even degree for all p. H a is a
finitely generated commutative kalgebra [13], and we let Va denote its as
sociated affine variety Max Hc. If M is any finitely generated kGmodule, then
the cohomologyvariety Vc(M) of M may be defined as the support in V~ of the
H~module H*(G,M) if G is a pgroup, and in general as the largest support of
H*(G,L where L is any kGmodule [4, 9]. A module L with each
irreducible kGmodule as a direct summand will serve.
D. Quillen [2022] proved a number of beautiful results relating V~to the va
