Contents Online
Homology, Homotopy and Applications
Volume 12 (2010)
Number 1
Algebraic cobordism and Grothendieck groups over singular schemes
Pages: 93 – 110
DOI: https://dx.doi.org/10.4310/HHA.2010.v12.n1.a8
Author
Abstract
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.
Keywords
algebraic cobordism, Grothendieck groups, singular schemes
2010 Mathematics Subject Classification
14C40, 14Fxx
Published 1 January 2010