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Finite homological dimension of \(BP_*(X)\) for infinite complexes. (English) Zbl 0535.55002

The main result proved in this paper states that for any finite \({\mathbb{Z}}_ p\)-complex X, \(BP_*(E{\mathbb{Z}}_ p\quad \times_{{\mathbb{Z}}_ p}X)\) has finite homological dimension. The proof uses the known fact that \(\hom \dim BP_*(B{\mathbb{Z}}_ p)=1,\) the standard projective resolution resulting from the Gysin sequence and several results on \(BP_*BP\)-comodules previously obtained by the author.
Reviewer: U.Würgler

MSC:

55N22 Bordism and cobordism theories and formal group laws in algebraic topology
55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology
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