Gross–Hopkins duals of higher real K–theory spectra

Barthel, Tobias; Beaudry, Agnès; Stojanoska, Vesna

doi:10.1090/tran/7730

Gross-Hopkins duals of higher real K-theory spectra

Authors: Tobias Barthel, Agnès Beaudry and Vesna Stojanoska
Journal: Trans. Amer. Math. Soc. 372 (2019), 3347-3368
MSC (2010): Primary 55M05, 55P42, 20J06, 55Q91, 55Q51, 55P60
DOI: https://doi.org/10.1090/tran/7730
Published electronically: May 30, 2019
MathSciNet review: 3988613
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Abstract: We determine the Gross-Hopkins duals of certain higher real -theory spectra. More specifically, let be an odd prime, and consider the Morava -theory spectrum of height . It is known, in expert circles, that for certain finite subgroups 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 which contain -torsion. This generalizes previous results for and .

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