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arXiv · 0905.4777

Gross-Hopkins duality and the Gorenstein condition

W. G. Dwyer·J. P. C. Greenlees·S. B. Iyengar
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Abstract

Gross and Hopkins have proved that in chromatic stable homotopy, Spanier-Whitehead duality nearly coincides with Brown-Comenetz duality. Our goal is to give a conceptual interpretation for this phenomenon in terms of the Gorenstein condition for maps of ring spectra in the sense of [Duality in algebra and topology, Adv. Math. 200 (2006), 357--402. arXiv: math.AT/0510247 ]. We describe a general notion of Brown-Comenetz dualizing module for a map of ring spectra and show that in this context such dualizing modules correspond bijectively to invertible K(n)-local spectra.

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W. G. Dwyer, J. P. C. Greenlees, S. B. Iyengar. 2010-08-28. Gross-Hopkins duality and the Gorenstein condition. https://arxiv.org/abs/0905.4777

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