### Algebraic Cobordism I, by Marc Levine and Fabien Morel

We define the notion of an oriented cohomology theory on
smooth, quasi-projective schemes over a field k, and construct,
in the case k has characteristic zero, the universal oriented
cohomology theory, which we call algebraic cobordism. We
compute the algebraic cobordism of the base field k, and show that
this is naturally isomorphic to the Lazard ring. We also verify a
localization property for algebraic cobordism. Using these facts,
we give a proof of Rost's degree formula and Rost's generalized
degree formula. Finally, we relate the algebraic cobordism of X to the
classical Chow ring of X and with the Grothendieck group of algebraic
vector bundles on X.

Marc Levine <marc@neu.edu>

Fabien Morel <morel@math.jussieu.fr>