Gorenstein duality for real spectra

Abstract

Following Hu and Kriz, we study the $C_2$–spectra $\mathit{BP}ℝ\langle n\rangle$ and $Eℝ\left(n\right)$ that refine the usual truncated Brown–Peterson and the Johnson–Wilson spectra. In particular, we show that they satisfy Gorenstein duality with a representation grading shift and identify their Anderson duals. We also compute the associated local cohomology spectral sequence in the cases $n=1$ and $2$.