Homotopy groups of homotopy fixed point spectra associated to E_n

Details Homotopy groups of homotopy fixed point spectra associated to E_n Homotopy groups of homotopy fixed point spectra associated to E_n

2009-03-25

arxiv.org/abs/0903.4290v1

Geom. Topol. Monogr. 10 (2007) 131-145

Mathematics

Algebraic Topology

This is the version published by Geometry & Topology Monographs on 29 January 2007

Scientific paper

10.2140/gtm.2007.10.131

We compute the mod(p) homotopy groups of the continuous homotopy fixed point spectrum E_2^{hH_2} for p>2, where E_n is the Landweber exact spectrum whose coefficient ring is the ring of functions on the Lubin-Tate moduli space of lifts of the height n Honda formal group law over F_{p^n}, and H_n is the subgroup WF^x_{p^n} wreath product Gal(F_{p^n}/F_p) of the extended Morava stabilizer group G_n. We examine some consequences of this related to Brown-Comenetz duality and to finiteness properties of homotopy groups of K(n)_*-local spectra. We also indicate a plan for computing pi_*(E_n^{hH_n} smash V(n-2)), where V(n-2) is an E_{n*}-local Toda complex.

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