Ravenel, Douglas C.; Wilson, W. Stephen; Yagita, Nobuaki Brown-Peterson cohomology from Morava \(K\)-theory. (English) Zbl 0912.55002 \(K\)-Theory 15, No. 2, 147-199 (1998). This paper gives the structure of the Brown-Peterson cohomology of a wide class of spaces – those with Morava \(K\)-theory concentrated in even dimensions. These spaces include: Eilenberg-Maclane spaces, loop spaces of finite Postnikov systems, and classifying spaces of most finite groups whose Morava \(K\)-theory is known. The main result is that for such spaces the Brown-Peterson cohomology is also concentrated in even dimensions and is flat as a \(BP^{*}\)-module for the category of finitely presented \(BP^{*}(BP)\)-modules. The proofs rely heavily on computations with the Atiyah-Hirzebruch spectral sequence. Reviewer: J.Hodgson (Philadelphia) Cited in 5 ReviewsCited in 23 Documents MSC: 55N15 Topological \(K\)-theory 19D10 Algebraic \(K\)-theory of spaces 55N22 Bordism and cobordism theories and formal group laws in algebraic topology 55P20 Eilenberg-Mac Lane spaces 19L20 \(J\)-homomorphism, Adams operations Keywords:Brown-Peterson cohomology; Morava \(K\)-theory; Eilenberg-Maclane spaces; Atiyah-Hirzebruch spectral sequence PDFBibTeX XMLCite \textit{D. C. Ravenel} et al., \(K\)-Theory 15, No. 2, 147--199 (1998; Zbl 0912.55002) Full Text: DOI