Tate cohomology lowers chromatic

Bousfield classes

Authors:
Mark Hovey and Hal Sadofsky

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3579-3585

MSC (1991):
Primary 55P60, 55P42; Secondary 55N91

DOI:
https://doi.org/10.1090/S0002-9939-96-03495-8

MathSciNet review:
1343699

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Abstract: Let be a finite group. We use recent results of J. P. C. Greenlees and H. Sadofsky to show that the Tate homology of local spectra with respect to produces local spectra. We also show that the Bousfield class of the Tate homology of (for finite) is the same as that of . To be precise, recall that Tate homology is a functor from -spectra to -spectra. To produce a functor from spectra to spectra, we look at a spectrum as a naive -spectrum on which acts trivially, apply Tate homology, and take -fixed points. This composite is the functor we shall actually study, and we'll prove that when is finite. When , the symmetric group on letters, this is related to a conjecture of Hopkins and Mahowald (usually framed in terms of Mahowald's functor ).

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Additional Information

**Mark Hovey**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Email:
hovey@math.mit.edu

**Hal Sadofsky**

Affiliation:
Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21230

Address at time of publication:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403

Email:
hs@math.jhu.edu, sadofsky@math.uoregon.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03495-8

Received by editor(s):
January 19, 1995

Received by editor(s) in revised form:
June 8, 1995

Additional Notes:
The authors were partially supported by the NSF

Communicated by:
Tom Goodwillie

Article copyright:
© Copyright 1996
American Mathematical Society