Essential cohomology for elementary abelian p-groups

Abstract

Communicated by M. Broué MSC: Primary: 20J06 13A50 55S10 a b s t r a c tFor an odd prime p the cohomology ring of an elementary abelian p-group is polynomial tensor exterior. We show that the ideal of essential classes is the Steenrod closure of the class generating the top exterior power. As a module over the polynomial algebra, the essential ideal is free on the set of Mùi invariants.