Search: MSC category 55N22
( Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] )
1. CJM 2014 (vol 67 pp. 639)
||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 cycles
Categories:14C17, 14F43, 55N22
2. CJM 2007 (vol 59 pp. 1154)
||$k(n)$-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.