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) 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 the Mahowald inverse limit lim ←− (P−k ∧ ΣE(n))). We also give a multiplicative splitting of tE(n) after a suitable base extension. AMS Classification numbers Primary: 55N22, 55P60 Secondary: 14L05

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