Gross-Hopkins duality and the Gorenstein condition

Details Gross-Hopkins duality and the Gorenstein condition Gross-Hopkins duality and the Gorenstein condition

2009-05-29

arxiv.org/abs/0905.4777v2

Mathematics

Algebraic Topology

27 pages. Introduction has been revised significantly; minor revisions elsewhere. To appear in the Journal of K-Theory

Scientific paper

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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