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 | References | Similar Articles | Additional Information
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