Landweber, Peter S. Finite homological dimension of \(BP_*(X)\) for infinite complexes. (English) Zbl 0535.55002 Proc. Am. Math. Soc. 84, 420-424 (1982). 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 Keywords:finite homological dimension PDFBibTeX XMLCite \textit{P. S. Landweber}, Proc. Am. Math. Soc. 84, 420--424 (1982; Zbl 0535.55002) Full Text: DOI