Homology, Homotopy and Applications

Volume 12 (2010)

Number 1

Algebraic cobordism and Grothendieck groups over singular schemes

Pages: 93 – 110

DOI: http://dx.doi.org/10.4310/HHA.2010.v12.n1.a8


Shouxin Dai (Department of Mathematics, University of California at Los Angeles)


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

14C40, 14Fxx

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