The topological nilpotence degree of a Noetherian unstable algebra

Abstract We investigate the topological nilpotence degree, in sense of Henn–Lannes–Schwartz, a connected Noetherian unstable algebra R . When is mod p cohomology ring compact Lie group, Kuhn showed how this invariant controlled by centralizers elementary abelian -subgroups. By replacing -subgroups with components Lannes’ T -functor, and utilizing techniques algebras over Steenrod algebra, we are able to generalize Kuhn’s result large class algebras. show generalizes more general classes groups, such as groups finite virtual cohomological dimension, profinite Kac–Moody groups. In fact, our results apply much generally, for example, establish -local Broto–Levi–Oliver, H -spaces cohomology, Borel equivariant group acting on manifold. Along way several independent interest. For formulate prove version Carlson’s depth conjecture case minimal depth.