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arXiv · 1705.07036

Gross-Hopkins Duals of Higher Real K-theory Spectra

Tobias Barthel·Agnes Beaudry·Vesna Stojanoska
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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 the 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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Tobias Barthel, Agnes Beaudry, Vesna Stojanoska. 2017-05-19. Gross-Hopkins Duals of Higher Real K-theory Spectra. https://doi.org/10.1090/tran%2F7730

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