Duality of classifying spaces in Morava K-theory

Rasmus Nørtoft Johansen

Titel: Duality of classifying spaces in Morava K-theory

Abstract: For any prime p and positive integer n there exists a 2(p^n - 1)-periodic cohomology theory K(n) known as Morava K-theory. These theories have been used for, among other things, studying complex cobordism theory. We describe the foundations of equivariant stable homotopy theory in terms of equivariant orthgonal spectra. We use this to provide a modern proof of a duality theorem for Morava K-theory which states that we have natural isomorphisms K(n)^*(BG) = K(n)_*(BG). In the process of doing this we will also prove a classical result of Ravenel that K(n)^*(BG) is finitely generated as a K(n)^*-module.

Supervisor: Irakli Patchkonia
Censor: Iver Ottosen, AAU