#### Geometry & Topology, Vol. 2 (1998)
Paper no. 8, pages 145--174.

## Completions of Z/(p)-Tate cohomology of periodic spectra

### Matthew Ando, Jack Morava, Hal Sadofsky

**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 Mahowald's inverse limit of P_{-k} smash SE(n)). We also give a multiplicative splitting of tE(n) after a suitable base extension.
**Keywords**.
Root invariant, Tate cohomology, periodicity, formal groups

**AMS subject classification**.
Primary: 55N22, 55P60.
Secondary: 14L05.

**DOI:** 10.2140/gt.1998.2.145

**E-print:** `arXiv:math.AT/9808141`

Submitted to GT on 5 September 1997.
(Revised 27 March 1998.)
Paper accepted 17 August 1998.
Paper published 17 August 1998.

Notes on file formats
Matthew Ando, Jack Morava, Hal Sadofsky

Department of Mathematics

Unversity of Virginia

Charlottesville, VA 22903

Department of Mathematics

The Johns Hopkins University

Baltimore, MD 21218

Department of Mathematics

University of Oregon

Eugene, OR 97403

Email: ma2m@faraday.clas.Virginia.edu, jack@math.jhu.edu, sadofsky@math.uoregon.edu

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