Algebraic cobordism and Grothendieck groups over singular schemes

Shouxin Dai

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.

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