Commutative algebra in the cohomology of groups

Three lectures given at the opening conference for the MSRI program
in commutative algebra, Sept 9-13, 2002.

Dave Benson
Department of Mathematics
University of Georgia
Athens GA 30602 
USA


Abstract.
Commutative algebra is used extensively in the cohomology of
groups. In this series of lectures, I shall concentrate on finite 
groups, but I shall also discuss the cohomology of finite group 
schemes, compact Lie groups, $p$-compact groups, infinite discrete
groups and profinite groups. I describe the role of various concepts 
from commutative algebra, including finite generation, Krull 
dimension, depth, associated primes, the Cohen--Macaulay and 
Gorenstein conditions, local cohomology, Grothendieck's local 
duality, and Castelnuovo--Mumford regularity.