A theorem of Levine-Morel states that algebraic cobordism groups are isomorphic to (multiplicative) Grothendieck groups over smooth schemes. We extend this theorem to singular schemes. As a consequence, we provide a new proof of the singular Riemann-Roch theorem of Baum-Fulton-MacPherson and a new type of Riemann-Roch theorem with respect to pullbacks of locally complete morphisms.
Homology, Homotopy and Applications, Vol. 12 (2010), No. 1, pp.93-110.
Available as: dvi dvi.gz ps ps.gz pdf