The Tate spectrum of the higher real K-theories at height n=p-1

2015/01/30 by Heard, Drew
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.07759

Abstract

Let E_n be Morava E-theory and let G ⊂ G_n be a finite subgroup of G_n, the extended Morava stabilizer group. Let E_n^tG be the Tate spectrum, defined as the cofiber of the norm map N:(E_n)_hG → E_n^hG. We use the Tate spectral sequence to calculate π_*E_p-1^tG for G a maximal finite p-subgroup, and p an odd prime. We show that E_p-1^tG ≃ ∗, so that the norm map gives equivalence between homotopy fixed point and homotopy orbit spectra. Our methods also give a calculation of π_*E_p-1^hG, which is a folklore calculation of Hopkins and Miller.

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