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Brown–Peterson cohomology from Morava
$E$-theory
- Part of
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- Journal:
- Compositio Mathematica / Volume 153 / Issue 4 / April 2017
- Published online by Cambridge University Press:
- 13 March 2017, pp. 780-819
- Print publication:
- April 2017
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- Article
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We prove that the
$p$-completed Brown–Peterson spectrum is a retract of a product of Morava 
$E$-theory spectra. As a consequence, we generalize results of Kashiwabara and of Ravenel, Wilson and Yagita from spaces to spectra and deduce that the notion of a good group is determined by Brown–Peterson cohomology. Furthermore, we show that rational factorizations of the Morava 
$E$-theory of certain finite groups hold integrally up to bounded torsion with height-independent exponent, thereby lifting these factorizations to the rationalized Brown–Peterson cohomology of such groups.
