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
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by Tobias Barthel, Agnès Beaudry and Vesna Stojanoska PDF

Trans. Amer. Math. Soc. 372 (2019), 3347-3368 Request permission

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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