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

Published online by Cambridge University Press:  20 June 2017

Drew Heard
Affiliation:
Department of Mathematics, Universität Hamburg, D-20146 Hamburg, Germany email drew.heard@uni-hamburg.de
Akhil Mathew
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA email amathew@math.harvard.edu
Vesna Stojanoska
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA email vesna@illinois.edu

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.

Type
Research Article
Copyright
© The Authors 2017 

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