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

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) $t E (n)$ 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 ${invlim}_{k} ((P_{- k} \land Σ E (n)))$ ). We also give a multiplicative splitting of $t E (n)$ after a suitable base extension.

Keywords

root invariant, Tate cohomology, periodicity, formal groups

Mathematical Subject Classification

Primary: 55N22, 55P60

Secondary: 14L05

References

Forward citations

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

Volume 2, issue 1 (1998)

Matthew Ando, Jack Morava and Hal Sadofsky