2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164924Relying on results of Hopkins-Morel, we show that, for $X$ a quasi-projective variety over a field of characteristic zero, the canonical map $Ω_n(X)\to MGL_{2n,n}'(X)$ is an isomorphism. Here $Ω_*(X)$ is the theory of algebraic cobordism defined by Levine-Morel, and $MGL_{*,*}'$ is the Borel-Moore homology version of the theory of algebraic cobordism defined via the algebraic Thom complex in the Morel-Voevodsky motivic stable homotopy category.22 pagesK-Theory and HomologyAlgebraic Topology14C25; 19E15text