Gross-Hopkins duality and the Gorenstein condition
Algebraic Topology
2010-08-31 v2 Commutative Algebra
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.
Cite
@article{arxiv.0905.4777,
title = {Gross-Hopkins duality and the Gorenstein condition},
author = {W. G. Dwyer and J. P. C. Greenlees and S. B. Iyengar},
journal= {arXiv preprint arXiv:0905.4777},
year = {2010}
}
Comments
27 pages. Introduction has been revised significantly; minor revisions elsewhere. To appear in the Journal of K-Theory