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Projectivity in Algebraic Cobordism

Published:2014-09-24

• Jose Luis Gonzalez,
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2
• Kalle Karu,
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2
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Abstract

The algebraic cobordism group of a scheme is generated by cycles that are proper morphisms from smooth quasiprojective varieties. We prove that over a field of characteristic zero the quasiprojectivity assumption can be omitted to get the same theory.
 Keywords: algebraic cobordism, quasiprojectivity, cobordism cycles
 MSC Classifications: 14C17 - Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14F43 - Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 55N22 - Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]