A Mini-Course on Morava Stabilizer Groups and Their Cohomology

Abstract

The Morava stabilizer groups play a dominating role in chromatic stable ho-motopy theory. In fact, for suitable spectra X, for example all finite spectra, thechromatic homotopy type of X at chromatic level n \textgreater{} 0 and a given prime p islargely controlled by the continuous cohomology of a certain p-adic Lie group Gn,in stable homotopy theory known under the name of Morava stabilizer group oflevel n at p, with coefficients in the corresponding Morava module (En)$\star$X.