2003/04/15 by Marc Levine · 1 citation
Mathematics · #math.KT #msc:19E15 #msc:14C99 #msc:14C25
published as Proceedings of the ICM, Beijing 2002, vol. 2, 57--66
arxiv created 2003/04/15 · arxiv updated 2009/11/30
Together with F. Morel, we have constructed in \citeCR, 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 ¶1-spectrum MGL in the Morel-Voevodsky stable homotopy category.