Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY
 

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
commutativefc-algebra,and we let VG denote its associated affine variety Max HG.
If M is any finitely generatedfcG-module,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 irreduciblefcG-moduleas 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 p-subgroups 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 fcG-module

  

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

 

Collections: Mathematics