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manuscripta mathematica

, Volume 29, Issue 1, pp 93–111 | Cite as

A splitting theorem for certain cohomology theories associated to BP* (−)

  • Urs Würgler
Article

Abstract

Let P(n)*(−) be Brown-Peterson cohomology modulo In and put B(n)*(−)=P(n)*(−)[1/vn]. In this note we construct a canonical multiplicative and idempotent operation Ωn in a suitable completion\(\bar B\) (n)*(−) of B(n)*(−) which has the property that its image is canonically isomorphic to the n-th Morava K-theory K(n)*(−). In particular, the ring theory K(n)*(−) is contained as a direct summand in the theory\(\bar B\) (n)*(−). A similar result is not true before completing. pleting. Because the completion map B (n)*(−) →\(\bar B\) (n)*(−) is injective, the above splitting theorem contains also information about B(n)*(−). The proof of the theorem depends on a result about the behaviour of formal groups of finite height over complete graded Fp.

Keywords

Number Theory Formal Group Algebraic Geometry Topological Group Direct Summand 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Urs Würgler
    • 1
  1. 1.Mathematisches InstitutUniversität BernBernSwitzerland

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