Gorenstein duality for Real spectra

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 $C_2$-spectra $BP\mathbb{R}\langle n \rangle$ and $E\mathbb{R}(n)$ 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 $2$.