Completions of Z/p-Tate cohomology of periodic spectra
Matthew Ando, Jack Morava and Hal Sadofsky
Classification numbers primary: 55N22, 55P60, secondary: 14L05
University of Virginia, Johns Hopkins University, University of Oregon
ma2m@faraday.clas.Virginia.edu, jack@math.jhu.edu, sadofsky@math.uoregon.edu
We construct splittings of some completions of the $\mathbf{Z}/
(p)$-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 $\mathbf{Z}/ (p)$-Tate cohomology spectrum
(i.e. the Mahowald inverse limit $\invlim{k}{(P_{-k} \wedge\Sigma E
(n))}$). We also give a multiplicative splitting of $tE (n)$ after a
suitable base extension.