### 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.

Original language | English (US) |
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Pages (from-to) | 3347-3368 |

Number of pages | 22 |

Journal | Transactions of the American Mathematical Society |

Volume | 372 |

Issue number | 5 |

DOIs | |

State | Published - Sep 1 2019 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Barthel, T., Beaudry, A., & Stojanoska, V. (2019). Gross–Hopkins duals of higher real K–theory spectra.

*Transactions of the American Mathematical Society*,*372*(5), 3347-3368. https://doi.org/10.1090/tran/7730