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

Following Hu and Kriz, we study the C2–spectra BPn and E(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.

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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
Received: 13 July 2016
Revised: 17 January 2017
Accepted: 1 February 2017
Published: 4 October 2017
J P C Greenlees
School of Mathematics and Statistics
University of Sheffield
United Kingdom
Lennart Meier
Mathematics Institute
University of Bonn