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A short proof of telescopic Tate vanishing

Authors: Dustin Clausen and Akhil Mathew
Journal: Proc. Amer. Math. Soc. 145 (2017), 5413-5417
MSC (2010): Primary 55P42, 55P47
Published electronically: June 16, 2017
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Abstract: We give a short proof of a theorem of Kuhn that Tate constructions for finite group actions vanish in telescopically localized stable homotopy theory. In particular, we observe that Kuhn's theorem is equivalent to the statement that the transfer $ BC_{p+} \to S^0$ admits a section after telescopic localization, which in turn follows from the Kahn-Priddy theorem.

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Additional Information

Dustin Clausen
Affiliation: Department of Mathematics, University of Copenhagen, Copenhagen, Denmark

Akhil Mathew
Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138

Received by editor(s): August 10, 2016
Received by editor(s) in revised form: December 16, 2016, and January 2, 2017
Published electronically: June 16, 2017
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2017 American Mathematical Society

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