#### Volume 2, issue 1 (1998)

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Completions of $\mathbb{Z}/(p)$–Tate cohomology of periodic spectra

### Matthew Ando, Jack Morava and Hal Sadofsky

Geometry & Topology 2 (1998) 145–174
 arXiv: math.AT/9808141
##### Abstract

We construct splittings of some completions of the $ℤ∕\left(p\right)$–Tate cohomology of $E\left(n\right)$ and some related spectra. In particular, we split (a completion of) $tE\left(n\right)$ as a (completion of) a wedge of $E\left(n-1\right)$s as a spectrum, where $t$ is shorthand for the fixed points of the $Z∕\left(p\right)$–Tate cohomology spectrum (ie the Mahowald inverse limit ${invlim}_{k}\left(\left({P}_{-k}\wedge \Sigma E\left(n\right)\right)\right)$). We also give a multiplicative splitting of $tE\left(n\right)$ after a suitable base extension.

##### Keywords
root invariant, Tate cohomology, periodicity, formal groups
##### Mathematical Subject Classification
Primary: 55N22, 55P60
Secondary: 14L05
##### 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