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Invent. math. 66, 277-286 (1982) [nvel~tlol~e$ matbematicae

Summary: Invent. math. 66, 277-286 (1982) [nvel~tlol~e$
,i" Springer-Vertag1982
Quillen Stratification for Modules
George S. Avrunin i and Leonard L. Scott .2
Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003,
2 Department of Mathematics, Universityof Virginia,Charlottesville,VA 22903, USA
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 [20-22] 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 k-algebra [13], and we let Va denote its as-
sociated affine variety Max Hc. If M is any finitely generated kG-module, 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 p-group, and in general as the largest support of
H*(G,L| where L is any kG-module [4, 9]. A module L with each
irreducible kG-module as a direct summand will serve.
D. Quillen [20-22] proved a number of beautiful results relating V~to the va-


Source: Avrunin, George S. - Department of Mathematics and Statistics, University of Massachusetts at Amherst


Collections: Mathematics