Gross-Hopkins Duals of Higher Real K-theory Spectra

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 $p=3$.

References in corpus (2)

• Topological resolutions in K(2)-local homotopy theory at the prime 2
• Picard groups of higher real $K$-theory spectra at height $p-1$

Cited by in corpus (1)

• Picard groups and duality for Real Morava $E$-theories