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Abstract:
Classical (oriented) cobordism is a generalized cohomology theory for
topological spaces, in fact the universal cohomology theory which posses
a projective bundle formula. As such, it maps to the more familiar
theories of singular cohomology and topological K-theory. Together with
Fabien Morel, I have developed a version of cobordism in algebraic
geometry, which has the relation to topological cobordism that algebraic
K_0 has to topological K-theory, and that the Chow ring has to singular
cohomology. In addition, one recovers algebraic K_0 and CH^* from our
algebraic cobordism. Finally, one can use algebraic cobordism to give a
proof of the so-called degree formulas of Markus Rost, which in turn
plays an important role in our understanding of the e'tale cohomology of
fields.
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