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The $C_2$-effective spectral sequence for $C_2$-equivariant connective real $K$-theory

Hana Jia Kong

Vol. 5 (2023), No. 4, 627–662
Abstract

We construct a C2-equivariant spectral sequence computing RO (C2)-graded homotopy groups by the C2-equivariant Betti realization functor realizing the motivic effective slice filtration. We apply the spectral sequence to compute the RO (C2)-graded homotopy groups of the completed C2-equivariant connective real K-theory spectrum. The computation reproves the C2-equivariant Adams spectral sequence results of Guillou, Hill, Isaksen and Ravenel. We also include the 2-Bockstein spectral sequence computation to compute the RO (C2)-graded homotopy ring of H2 ¯ from that of H𝔽2 ¯.

Keywords
motivic stable homotopy theory, spectral sequence, K-theory
Mathematical Subject Classification
Primary: 19E15, 55Q91, 55T25
Milestones
Received: 13 August 2022
Revised: 9 May 2023
Accepted: 24 May 2023
Published: 21 November 2023
Authors
Hana Jia Kong
School of Mathematics
Institute for Advanced Study
Princeton, NJ
United States