Algebraic cobordism

Details Algebraic cobordism Algebraic cobordism

2003-04-15

arxiv.org/abs/math/0304206v1

Proceedings of the ICM, Beijing 2002, vol. 2, 57--66

Mathematics

K-Theory and Homology

Scientific paper

Together with F. Morel, we have constructed in \cite{CR, Cobord1, Cobord2} a theory of {\em algebraic cobordism}, an algebro-geometric version of the topological theory of complex cobordism. In this paper, we give a survey of the construction and main results of this theory; in the final section, we propose a candidate for a theory of higher algebraic cobordism, which hopefully agrees with the cohomology theory represented by the $\P^1$-spectrum $MGL$ in the Morel-Voevodsky stable homotopy category.

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