Total power operations in spectral sequences

Balderrama, William

doi:10.1090/tran/9073

Total power operations in spectral sequences
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by William Balderrama;

Trans. Amer. Math. Soc. 377 (2024), 4779-4823

DOI: https://doi.org/10.1090/tran/9073

Published electronically: May 17, 2024

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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 $\pi _0$ 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.

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Total power operations in spectral sequences
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Abstract: