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Picard groups of higher real $K$ -theory spectra at height $p-1$

  • Drew Heard (a1), Akhil Mathew (a2) and Vesna Stojanoska (a3)

Abstract

Using the descent spectral sequence for a Galois extension of ring spectra, we compute the Picard group of the higher real $K$ -theory spectra of Hopkins and Miller at height $n=p-1$ , for $p$ an odd prime. More generally, we determine the Picard groups of the homotopy fixed points spectra $E_{n}^{hG}$ , where $E_{n}$ is Lubin–Tate $E$ -theory at the prime $p$ and height $n=p-1$ , and $G$ is any finite subgroup of the extended Morava stabilizer group. We find that these Picard groups are always cyclic, generated by the suspension.

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Picard groups of higher real $K$ -theory spectra at height $p-1$

  • Drew Heard (a1), Akhil Mathew (a2) and Vesna Stojanoska (a3)

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