RO(G)-graded homotopy fixed point spectral sequence for height 2 Morava E-theory

2022/09/05 by Duan, Zhipeng, Kong, Hana Jia, Li, Guchuan +2 · 1 citation
#20J06 #55P42 #55P60 #55Q91 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.01830

Abstract

We consider G=Q₈,SD₁₆,G₂₄, and G₄₈ as finite subgroups of the Morava stabilizer group which acts on the height 2 Morava E-theory E₂ at the prime 2. We completely compute the G-homotopy fixed point spectral sequences of E₂. Our computation uses recently developed equivariant techniques since Hill, Hopkins, and Ravenel. We also compute the (*-σ_i)-graded Q₈- and SD₁₆-homotopy fixed point spectral sequences, where σ_i is a non-trivial one-dimensional representation of Q₈.

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• Periodicity and finite complexity in higher real K-theories

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