Algebraic cobordism
Abstract
Together with F. Morel, we have constructed in CR, Cobord1, Cobord2 a theory of 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 1-spectrum MGL in the Morel-Voevodsky stable homotopy category.
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