TOTAL POWER OPERATIONS IN SPECTRAL SEQUENCES

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 It0 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 which may be of independent interest.