#### 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