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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Gross-Hopkins duals of higher real K-theory spectra


Authors: Tobias Barthel, Agnès Beaudry and Vesna Stojanoska
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 55M05, 55P42, 20J06, 55Q91, 55Q51, 55P60
DOI: https://doi.org/10.1090/tran/7730
Published electronically: May 30, 2019
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Abstract: We determine the Gross-Hopkins duals of certain higher real $ K$-theory spectra. More specifically, let $ p$ be an odd prime, and consider the Morava $ E$-theory spectrum of height $ n=p-1$. It is known, in expert circles, that for certain finite subgroups $ G$ of the Morava stabilizer group, the homotopy fixed point spectra $ E_n^{hG}$ are Gross-Hopkins self-dual up to a shift. In this paper, we determine the shift for those finite subgroups $ G$ which contain $ p$-torsion. This generalizes previous results for $ n=2$ and $ p=3$.


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Additional Information

Tobias Barthel
Affiliation: Department of Mathematics, University of Copenhagen, DK-2100 Copenhagen, Denmark

Agnès Beaudry
Affiliation: Department of Mathematics, University of Colorado Boulder, Boulder, Colorado 80309

Vesna Stojanoska
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

DOI: https://doi.org/10.1090/tran/7730
Received by editor(s): May 19, 2017
Received by editor(s) in revised form: July 19, 2018, and October 17, 2018
Published electronically: May 30, 2019
Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No. DMS-1606479 and Grant No. DMS-1612020/1725563.
The first-named author was partially supported by the DNRF92.
Article copyright: © Copyright 2019 American Mathematical Society