Gorenstein duality for real spectra

Following Hu and Kriz, we study the C 2 -spectra BPℝ⟨n⟩hni and Eℝ(n) 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.