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Projectivity in Algebraic Cobordism

Published online by Cambridge University Press:  20 November 2018

Jose Luis Gonzalez  and
Kalle Karu
Jose Luis Gonzalez
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2 e-mail: jgonza@math.ubc.ca, karu@math.ubc.ca
Kalle Karu
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2 e-mail: jgonza@math.ubc.ca, karu@math.ubc.ca
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Abstract

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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

14C1714F4355N22algebraic cobordismquasiprojectivitycobordism cycles
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 3 , 01 June 2015 , pp. 639 - 653
Copyright
Copyright © Canadian Mathematical Society 2015

References

[1] Abramovich, D., Karu, K., Matsuki, K., and Wlodarczyk, J., Torification and factorization of birational maps. J. Amer. Math. Soc. 15(2002), no. 3, 531–572 (electronic).http://dx.doi.org/10.1090/S0894-0347-02-00396-X Google Scholar
[2] González, J. and Karu, K., Descent for algebraic cobordism. arxiv:1301.3292Google Scholar
[3] Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II. Ann. of Math. (2) 9(1964), 109–203; ibid (2) 79(1964), 205–326.Google Scholar
[4] Levine, M. and Morel, F., Algebraic cobordism. Springer Monographs in Mathematics, Springer, Berlin, 2007.Google Scholar
[5] Levine, M. and Pandharipande, R., Algebraic cobordism revisited. Invent. Math. 176(2009), no. 1, 63–130.http://dx.doi.org/10.1007/s00222-008-0160-8 Google Scholar
[6] Wlodarczyk, J., Toroidal varieties and the weak factorization theorem. Invent. Math. 154(2003), no. 2, 223–331. http://dx.doi.org/10.1007/s00222-003-0305-8 Google Scholar