Completions of Ζ/(p)-Tate cohomology of periodic spectra

Matthew Ando; Jack Morava; Hal Sadofsky

doi:10.2140/gt.1998.2.145

Completions of Ζ/(p)-Tate cohomology of periodic spectra

Matthew Ando, Jack Morava, Hal Sadofsky

Research output: Contribution to journal › Article › peer-review

Abstract

We construct splittings of some completions of the Ζ/(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 Ζ/(p)-Tate cohomology spectrum (ie the Mahowald inverse limit lim_←k (P^-k Λ ΣE(n))). We also give a multiplicative splitting of tE(n) after a suitable base extension.

Original language	English (US)
Pages (from-to)	145-174
Number of pages	30
Journal	Geometry and Topology
Volume	2
DOIs	https://doi.org/10.2140/gt.1998.2.145
State	Published - 1998
Externally published	Yes

Keywords

Formal groups
Periodicity
Root invariant
Tate cohomology

ASJC Scopus subject areas

Geometry and Topology

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10.2140/gt.1998.2.145

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AU - Ando, Matthew

AU - Morava, Jack

AU - Sadofsky, Hal

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AB - We construct splittings of some completions of the Ζ/(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 Ζ/(p)-Tate cohomology spectrum (ie the Mahowald inverse limit lim←k (P-k Λ ΣE(n))). We also give a multiplicative splitting of tE(n) after a suitable base extension.

KW - Formal groups

KW - Periodicity

KW - Root invariant

KW - Tate cohomology

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JO - Geometry and Topology

JF - Geometry and Topology

ER -

Completions of Ζ/(p)-Tate cohomology of periodic spectra

Abstract

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