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arXiv · 1509.05678

Brown-Peterson cohomology from Morava E-theory

Tobias Barthel·Nathaniel Stapleton
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Abstract

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 Ravenel-Wilson-Yagita and Kashiwabara from spaces to spectra and deduce that the notion of 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.

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BibTeXRIS

Tobias Barthel, Nathaniel Stapleton. 2015-09-18. Brown-Peterson cohomology from Morava E-theory. https://doi.org/10.1112/s0010437x16008241

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