Voevodsky's conjecture that algebraic cobordism is logarithmic

Let $S\in\mathrm{Rg}$ be a base ring, and let $\mathrm{SH}(S)$ denote the stable motivic homotopy category over $S$. Let $\mathbf{MGL}\in\mathrm{SH}(S)$ be the algebraic cobordism spectrum due to Voevodsky. A cohomology theory is logarithmic when it satisfies the logarithmic extension property defined in the paper. Voevodsky's logarithmic algebraic cobordism conjecture. The algebraic cobordism spectrum $\mathbf{MGL}$ is logarithmic. The conjecture is presented as technically more demanding than the preceding theorem, with the required computations involving algebraic cobordism of toric varieties; its resolution is not supplied.