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Detruncating Morava K-theory. (English) Zbl 0751.55003

Adams memorial symposium on algebraic topology, vol. 2, Proc. Symp., Manchester/UK 1990, Lond. Math. Soc. Lect. Note Ser. 176, 35-43 (1992).
[For the entire collection see Zbl 0743.00067.]
For each prime \(p\) and \(n>0\) there is a cohomology theory \(BP\langle n\rangle^*(-)\) with coefficients \(BP\langle n\rangle_ *=BP_ */(v_ k: k>n)\). If \(E(n)=v_ n^{-1}BP\langle n\rangle\) let \(\widehat{E(n)}\) denote the Artinian completion of \(E(n)\). Theorem: If \(p\) is odd and \(X\) a finite complex with \(K(n)^{odd}(X)=0\) then there is a space \(Y\) whose \(K(n)\)-cohomology is a formal power series algebra over \(K(n)_ *\), and a map \(e: X\to Y\) giving an epimorphism in \(K(n)^*(-)\). — An important step in the proof is the fact that under the above assumptions \(K(n)^*(X)\) can be lifted to \(\widehat{E(n)}^*(X)\). The space \(Y\) is a product of certain spaces in the \(\Omega\)-spectrum for \(BP\langle n\rangle\).

MSC:

55N15 Topological \(K\)-theory

Citations:

Zbl 0743.00067
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