Gorenstein duality for Real spectra
J.P.C.Greenlees, Lennart Meier

TL;DR
This paper investigates Gorenstein duality properties of certain $C_2$-spectra that refine classical spectra, identifying their Anderson duals and computing related spectral sequences for specific cases.
Contribution
It establishes Gorenstein duality for $BP\mathbb{R}\langle n \rangle$ and $E\mathbb{R}(n)$ spectra, and computes their local cohomology spectral sequences for $n=1,2$.
Findings
Gorenstein duality holds for the studied spectra with a specific shift.
Identification of Anderson duals for these spectra.
Explicit computation of local cohomology spectral sequences for $n=1,2$.
Abstract
Following Hu and Kriz, we study the -spectra and 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 and .
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