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Uniqueness of Morava K-theory
- Part of
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- Journal:
- Compositio Mathematica / Volume 147 / Issue 2 / March 2011
- Published online by Cambridge University Press:
- 27 September 2010, pp. 633-648
- Print publication:
- March 2011
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- Article
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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.
-algebra structures. Here 
is the 