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Uniqueness of Morava K-theory

Published online by Cambridge University Press:  27 September 2010

Vigleik Angeltveit*
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA (email: vigleik@math.uchicago.edu)
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Abstract

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We show that there is an essentially unique S-algebra structure on the Morava K-theory spectrum K(n), while K(n) has uncountably many MU or -algebra structures. Here is the K(n)-localized Johnson–Wilson spectrum. To prove this we set up a spectral sequence computing the homotopy groups of the moduli space of A structures on a spectrum, and use the theory of S-algebra k-invariants for connectiveS-algebras found in the work of Dugger and Shipley [Postnikov extensions of ring spectra, Algebr. Geom. Topol. 6 (2006), 1785–1829 (electronic)] to show that all the uniqueness obstructions are hit by differentials.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2010

References

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