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 C_2 -equivariant Adams spectral sequence, to compute norms on π 0 \pi _0 of the equivariant K U KU -local sphere, and to compute power operations for the K ( 1 ) K(1) -local sphere. An appendix contains material on equivariant Bousfield localizations which may be of independent interest.