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Characteristic classes determine dualizing modules

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HHHW03 - Derived algebraic geometry and chromatic homotopy theory

I will address the question of determining the K(n)-local Spanier-Whitehead dual of the Lubin-Tate spectrum, equivariantly with respect to the action of the Morava stabilizer group. A dualizing module can be constructed abstractly, and we use characteristic classes to relate it to a certain representation sphere, at least when we restrict the action to a finite subgroup. As a consequence in specific examples, explicit calculations of characteristic classes also give explicit formulas for the Spanier-Whitehead duals of spectra like TMF and higher real K-theories. This is work in progress, joint with Agnes Beaudry, Paul Goerss, and Mike Hopkins.

This talk is part of the Isaac Newton Institute Seminar Series series.

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