Cohomology

Abstract

. We compute the continuous cohomology of the Morava stabilizer group with coefficients in Morava E -theory, H ∗ ( G 2 , E t ), at p = 2, for 0 ≤ t < 12, using the Algebraic Duality Spectral Sequence. Furthermore, in that same range, we compute the d 3 -differentials in the homotopy fixed point spectral sequence for the K (2)-local sphere spectrum. These cohomology groups and differentials play a central role in K (2)-local stable homotopy theory, in particular for the analysis of the K (2)-local Picard group.