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Using the descent spectral sequence for a Galois extension of ring spectra, we compute the Picard group of the higher real
-theory spectra of Hopkins and Miller at height
an odd prime. More generally, we determine the Picard groups of the homotopy fixed points spectra
-theory at the prime
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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