Volume 17, issue 6 (2017)

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Gorenstein duality for real spectra

J P C Greenlees and Lennart Meier

Algebraic & Geometric Topology 17 (2017) 3547–3619
Abstract

Following Hu and Kriz, we study the ${C}_{2}$–spectra $\mathit{BP}ℝ〈n〉$ 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 $2$.

Keywords
Anderson duality, Gorenstein duality, real K-theory, real bordism, real Brown-Peterson spectra, real Johnson-Wilson theories
Mathematical Subject Classification 2010
Primary: 55P91, 55U30
Secondary: 55P43, 55Q91