Homology, Homotopy and Applications
Volume 12 (2010)
Algebraic cobordism and Grothendieck groups over singular schemes
Pages: 93 – 110
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.
algebraic cobordism; Grothendieck groups; singular schemes
2010 Mathematics Subject Classification