Total power operations in spectral sequences

Abstract

We describe how power operations descend through homotopy limit spectral sequences. We apply this to describe how norms appear in the C 2 -equivariant Adams spectral sequence, to compute norms on π 0 of the equivariant KU -local sphere, and to compute power operations for the K(1)-local sphere. An appendix contains material on equivariant Bousfield localizations that may be of independent interest. Contents 1. Introduction 2. Unstable naturality of the homotopy limit spectral sequence 3. Looping power operations 4. Norms in the C 2 -equivariant Adams spectral sequence 5. Norms on π 0 of the equivariant KU -local sphere 6. Power operations for the K(1)-local sphere Appendix A. Equivariant Bousfield localizations References