Volume 10 (2007)

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Homotopy groups of homotopy fixed point spectra associated to En

Ethan S Devinatz

Geometry & Topology Monographs 10 (2007) 131–145

DOI: 10.2140/gtm.2007.10.131

arXiv: 0903.4290

Abstract

We compute the mod(p) homotopy groups of the continuous homotopy fixed point spectrum EhH22 for p>2, where En 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 Fpn, and Hn is the subgroup WF×pn⋊Gal(Fpn/Fp) of the extended Morava stabilizer group Gn. 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 π*(EhHnn∧V(n-2)), where V(n-2) is an En*–local Toda complex.

Keywords

Brown–Peterson homology, Morava stabilizer group, K(n)*–local homotopy theory

Mathematical Subject Classification

Primary: 55Q10, 55T25

References
Publication

Received: 13 September 2004
Revised: 5 July 2005
Published: 29 January 2007

Authors
Ethan S Devinatz
Department of Mathematics
University of Washington
Seattle
Washington
USA
http://www.math.washington.edu/~devinatz/