Gorenstein duality for real spectra

Greenlees, J P C; Meier, Lennart

doi:10.2140/agt.2017.17.3547

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Gorenstein duality for real spectra

J P C Greenlees and Lennart Meier

Algebraic & Geometric Topology 17 (2017) 3547–3619

DOI: 10.2140/agt.2017.17.3547

Abstract

Following Hu and Kriz, we study the $C_{2}$ –spectra $BP ℝ 〈 n 〉$ and $E ℝ (n)$ 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 $2$ .

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

References

Publication

Received: 13 July 2016

Revised: 17 January 2017

Accepted: 1 February 2017

Published: 4 October 2017

Authors

J P C Greenlees
School of Mathematics and Statistics University of Sheffield Sheffield United Kingdom

Lennart Meier
Mathematics Institute University of Bonn Bonn Germany

Volume 17, issue 6 (2017)