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Journal of the London Mathematical Society Advance Access originally published online on October 27, 2007
Journal of the London Mathematical Society 2007 76(3):586-604; doi:10.1112/jlms/jdm056
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© 2007 London Mathematical Society

Algebraic cobordisms of a Pfister quadric

A. Vishik

School of Mathematical Sciences
University of Nottingham
University Park
Nottingham, NG7 2RD
United Kingdom
alexander.vishik{at}nottingham.ac.uk

N. Yagita

Faculty of Education
Ibaraki University
Mito, Ibaraki
Japan
yagita{at}mx.ibaraki.ac.jp

In this article we compute the ring of algebraic cobordisms of a Pfister quadric. This is a rare example of a non-cellular variety where such a computation is known. We consider the algebraic cobordisms {Omega}* of Levine and Morel, as well as the MGL2*, * of Voevodsky. The methods of computation in these two cases are quite different. However, the results do agree (which supports the expectation that the two theories actually coincide). We show that the restriction homomorphism in our case is injective for any field extension E/F.

2000 Mathematics Subject Classification 11E04, 14C15, 14F42, 19E15, 55N20, 55N22.

The first author was supported by the Weyl Fund and by RFBR grant 22005.

Received October 5, 2005; revised November 28, 2006; published online October 27, 2007.


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