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Search: MSC category 55N22 ( Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] )

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1. CJM Online first

Gonzalez, Jose Luis; Karu, Kalle
 Projectivity in Algebraic Cobordism The algebraic cobordism group of a scheme is generated by cycles that are proper morphisms from smooth quasiprojective varieties. We prove that over a field of characteristic zero the quasiprojectivity assumption can be omitted to get the same theory. Keywords:algebraic cobordism, quasiprojectivity, cobordism cyclesCategories:14C17, 14F43, 55N22

2. CJM 2007 (vol 59 pp. 1154)

Boardman, J. Michael; Wilson, W. Stephen
 \$k(n)\$-Torsion-Free \$H\$-Spaces and \$P(n)\$-Cohomology The \$H\$-space that represents Brown--Peterson cohomology \$\BP^k (-)\$ was split by the second author into indecomposable factors, which all have torsion-free homotopy and homology. Here, we do the same for the related spectrum \$P(n)\$, by constructing idempotent operations in \$P(n)\$-cohomology \$P(n)^k (\$--\$)\$ in the style of Boardman--Johnson--Wilson; this relies heavily on the Ravenel--Wilson determination of the relevant Hopf ring. The resulting \$(i- 1)\$-connected \$H\$-spaces \$Y_i\$ have free connective Morava \$\K\$-homology \$k(n)_* (Y_i)\$, and may be built from the spaces in the \$\Omega\$-spectrum for \$k(n)\$ using only \$v_n\$-torsion invariants. We also extend Quillen's theorem on complex cobordism to show that for any space \$X\$, the \linebeak\$P(n)_*\$-module \$P(n)^* (X)\$ is generated by elements of \$P(n)^i (X)\$ for \$i \ge 0\$. This result is essential for the work of Ravenel--Wilson--Yagita, which in many cases allows one to compute \$\BP\$-cohomology from Morava \$\K\$-theory. Categories:55N22, 55P45