Uniqueness of Morava K-theory
Date
2011
Authors
Angeltveit, Vigleik
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Volume Title
Publisher
London Mathematical Society
Abstract
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 E(n)-algebra structures. Here E(n) 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.
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Keywords
Keywords: moduli space; Morava K-theory; S-algebra
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Source
Compositio Mathematica
Type
Journal article
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Restricted until
2037-12-31
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