Abstract
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In this mostly expository note we take advantage of homotopical and
algebraic advances to give a modern account of power operations on the mod
homology
of
–ring
spectra. The main advance is a quick proof of the Adem relations utilizing the
Tate-valued Frobenius as a homotopical incarnation of the total power operation. We
also give a streamlined derivation of the action of power operations on the dual
Steenrod algebra.
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Keywords
power operations, Dyer–Lashof operations, Steenrod algebra,
Nishida relations, Adem relations, Tate Frobenius
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Mathematical Subject Classification
Primary: 55P43, 55S12
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Publication
Received: 26 November 2020
Revised: 5 February 2022
Accepted: 15 May 2022
Published: 26 September 2023
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© 2023 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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