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Completions of Z⁄(p)–Tate cohomology of periodic spectra

Matthew Ando, Jack Morava and Hal Sadofsky

Geometry & Topology 2 (1998) 145–174

DOI: 10.2140/gt.1998.2.145

arXiv: math.AT/9808141
Abstract

We construct splittings of some completions of the Z ∕ (p)–Tate cohomology of E(n) and some related spectra. In particular, we split (a completion of) tE(n) as a (completion of) a wedge of E(n − 1)s as a spectrum, where t is shorthand for the fixed points of the Z ∕ (p)–Tate cohomology spectrum (ie the Mahowald inverse limit invlimk((P−k ∧ ΣE(n)))). We also give a multiplicative splitting of tE(n) after a suitable base extension.

Keywords

root invariant, Tate cohomology, periodicity, formal groups
Mathematical Subject Classification

Primary: 55N22, 55P60

Secondary: 14L05
References
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Publication

Received: 5 September 1997
Revised: 27 March 1998
Accepted: 17 August 1998
Published: 17 August 1998
Proposed: Haynes Miller
Seconded: Ralph Cohen, Gunnar Carlsson
Authors
Matthew Ando
Department of Mathematics, University of Virginia
Charlottesville
Virginia 22903
USA
Jack Morava
Department of Mathematics
The Johns Hopkins University
Baltimore
Maryland 21218
USA
Hal Sadofsky
Department of Mathematics
University of Oregon
Eugene
Oregon 97403
USA